MCAT Physics Review

Contents:

Translational Motion

Dimensions (length or distance, time) Vectors, components Vector addition Speed, velocity (average and instantaneous) Acceleration Freely falling bodies

Force and Motion, Gravitation

Center of mass Newton's first law, inertia Newton's second law (F = ma) Newton's third law, forces equal and opposite Concept of a field Law of gravitation (F = Gm1m2/r^2) Uniform circular motion Centripetal Force (F=mv2/r) Weight Friction, static and kinetic Motion on an inclined plane Analysis of pulley systems Force

Equilibrium and Momentum

Equilibriumo Concept of force, unitso Translational equilibrium (Sum of Fi = 0)o Rotational equilibrium (Sum of Torque = 0)o Analysis of forces acting on an objecto Newton's first law, inertiao Torques, lever armso Weightlessness

Momentumo Momentum = mvo Impulse = Fto Conservation of linear momentumo Elastic collisionso Inelastic collisions

Work and Energy

Work

o Derived units, sign conventionso Amount of work done in gravitational field is path-independento Mechanical advantageo Work-kinetic energy theoremo Power

Energyo Kinetic energy: KE = 1/2 mv^2; unitso Potential energy

PE = mgh (gravitational, local) PE = 1/2kx^2 (spring) PE = -GmM/r (gravitational, general)

o Conservation of energyo Conservative forceso Power, units

Waves and Periodic Motion

Periodic motiono Amplitude, period, frequencyo Phaseo Hooke's law, force F= -kxo Simple harmonic motion; displacement as a sinusoidal function of timeo Motion of a pendulumo General periodic motion: velocity, amplitude

Wave Characteristicso Transverse and longitudinal waveso Wavelength, frequency, velocityo Amplitude, intensityo Supposition of waves, interference, additiono Resonanceo Standing waves, nodeso Beat frequencieso Refraction and diffraction

Sound

Production of sound Relative speed of sound in solids, liquids and gases Intensity of sound (decibel units, log scale) Attenuation Doppler effect (moving sound source or observer, reflection of sound from a moving object) Pitch Resonance in pipes and strings Harmonics Ultrasound

Fluids and Solids

Fluidso Density, specific gravityo Buoyancy, Archimedes' principle

o Hydrostatic pressure Pascal's law P = pgh (pressure vs. depth)

o Viscosity: Poiseuille flowo Continuity equation (A·v = constant)o Concept of turbulence at high velocitieso Surface tensiono Bernoulli's equation

Solidso Densityo Elastic properties (elementary properties)o Elastic limito Thermal expansion coefficiento Shearo Compression

Electrostatics and Electromagnetism

Electrostaticso Charge, conductors, charge conservationo Insulatorso Coulomb's law (F = kq1q2/r2, sign conventions)o Electric field

field lines field due to charge distribution

o Potential difference, absolute potential at point in spaceo Equipotential lineso Electric dipole

definition of dipole behavior in electric field potential due to dipole

o Electrostatic inductiono Gauss' law

Magnetismo Definition of the magnetic field Bo Existence and direction of force on charge moving in magnetic field

Electromagnetic Radiation (Light)o Properties of electromagnetic radiation (general properties only)

radiation velocity equals constant c, in vacuo radiation consists of oscillating electric and magnetic fields that are mutually perpendicular to

each other and to the propagation directiono Classification of electromagnetic spectrum (radio, infrared, UV, X-rays, etc.)

Electronic Circuit Elements

Circuit elementso Current (I = ΔQ/Δt, sign conventions, units)o Battery, electromotive force, voltageo Terminal potential, internal resistance of batteryo Resistance

Ohm's law (I = V/R) resistors in series

resistors in parallel resistivity (ρ = RA/L)

o Capacitance concept of parallel-plate capacitor energy of charged capacitor capacitors in series capacitors in parallel dielectric

o Discharge of a capacitor through a resistoro Conductivity theory

Circuitso Power in circuits (P = VI, P = I2R)

Alternating Currents and Reactive Circuitso Root-mean-square currento Root-mean-square voltage

Light and Geometrical Optics

Light (Electromagnetic Radiation)o Concept of interference, Young double slit experimento Thin films, diffraction grating, single slit diffractiono Other diffraction phenomena, X-ray diffractiono Polarization of lighto Doppler effect (moving light source or observer)o Visual spectrum, color

energy lasers

Geometrical Opticso Reflection from plane surface (angle of incidence equals angle of reflection)o Refraction, refractive index n, Snell's law (n1sinθ1 = n2sinθ2)o Dispersion (change of index of refraction with wavelength)o Conditions for total internal reflectiono Spherical mirrors

mirror curvature, radius, focal length use of formula (1/p) + (1/q) = 1/f with sign conventions real and virtual images

o Thin lenses converging and diverging lenses, focal length use of formula (1/p) + (1/q) = 1/f, with sign conventions real and virtual images lens strength, diopters lens aberration

o Combination of lenseso Ray tracingo Optical instruments

Atomic and Nuclear Structure (Physics portion)

Atomic Structure and Spectrao Emission spectrum of hydrogen (Bohr model)o Atomic energy levels

quantized energy levels for electrons

calculation of energy emitted or absorbed when an electron changes energy levels Atomic Nucleus

o Atomic number, atomic weighto Neutrons, protons, isotopeso Nuclear forceso Radioactive decay: alpha, beta, gamma, half-life, stability, exponential decay, semi-log plotso General nature of fissiono General nature of fusiono Mass deficit, energy liberated, binding energy

Old AAMC Topics: the topics below have either been removed or modified from the original AAMC topic.

Magnetism

Orbits of charged particles moving in magnetic field General concepts of sources of the magnetic field Nature of solenoid, toroid Ampere's law for magnetic field induced by current in straight wire and other simple configurations Comparison of E and B relations

o force of B on a currento energy

Basic Concepts and General Techniques (old aamc topic)

This entire section has been taken out of the official aamc topics list.

Units and dimensionso Metric units:

conversions within metric system conversion from metric to English units conversion within English system

o Dimensional balance, checking equations for dimensional correctnesso Significant figureso Numerical estimation

Basic conceptso Mass, length, timeo Role of experiment and measurement

Graphing techniqueso Cartesian co-ordinate systemo Use of semi-log graph papero Use of log-log graph paper

Error analysiso Random vs. systematic errorso Propagation of errorso Mean and standard deviationo Chio Student t

Translational Motion

Dimensions (length or distance, time)

One dimension = magnitude of length or distance only. Two dimensions = length or distance on a 2D plane (xy coordinates). Three dimensions = length or distance in 3D space (xyz coordinates). Four dimensions = length or distance in 3D space at a given time (xyzt coordinates).

Vectors, components

Scalar: without direction. For example, length, time, mass. Vector: with direction. For example, displacement, acceleration, force. Components: the portion of the vector in a given direction.

Trigonometric rules:o SOH CAH TOA = silly old Harry, caught a herring, trolling off Anglesea.o SOH: sinθ = opposite / hypotenus.o CAH: cosθ = adjacent / hypotenus.o TOA: tanθ = opposite / adjacent.

Vector addition

You can only directly add vectors if they are in the same direction. To add vectors in different directions, you must add their x, y and z components. The resulting components

make up the added vector. The vector sum of all components of a vector equal to the vector itself. Operation involving a vector and a vector may or may not result in a vector (kinetic energy from the square of

vector velocity results in scalar energy). Operation involving a vector and a scalar always results in a vector. Operation involving a scalar and a scalar always results in a scalar.

Speed, velocity (average and instantaneous)

Speed: scalar, no direction, rate of change in distance. Velocity: vector, has direction, rate of change in displacement.

Average speed:

Average velocity: Instantaneous speed is the speed at an instant (infinitesimal time interval). Instantaneous velocity is the velocity at an instant (infinitesimal time interval). Instantaneous speed equals instantaneous velocity in magnitude. Instantaneous velocity has a direction, instantaneous speed does not. The direction of instantaneous velocity is tangent to the path at that point.

Acceleration

Acceleration is rate of the change

Average acceleration:o Uniformly accelerated motion along a straight lineo If acceleration is constant and there is no change in direction, all the following applies:o The value of speed/velocity, distance/displacement are interchangeable in this case, just keep a mental

note of the direction.

o

o

oo

ooo You need to memorize those, be able to rearrange them, combine them, and how to use them.o You need to assign one direction as + and the opposite as -, and then keep this scheme for all your

calculations.o For Cartesian coordinates, take upward and rightward motion as positive; down and left as negative.o For free falls, take downward as positive.o You can assign in what ever fashion you want, as long as the opposite direction is opposite in sign.

Freely falling bodies

Free falling objects move toward the ground at constant acceleration. On Earth, the rate of acceleration is g, which is 9.8 m/s2. Whenever something is in the air, it's in a free fall, even when it is being tossed upwards, downwards or at an

angle. For things being dropped, it's easier if you take down as positive, since that will make g positive. For things being tossed downwards, it's easier if you take down as positive, since that will make both initial

velocity and g positive. For things being tossed upwards, the initial velocity will have opposite sign as g. You can take either up or down

as positive depending on the question and what's convenient, but either way, initial velocity will have oppositesigns as g.

The acceleration due to gravity is constant because the force (weight) and mass of the object is constant. The net acceleration is a constant g if you don't take air resistance into consideration. Usually questions ignore

air resistance. But if the question gives you air resistance, then the acceleration is no longer constant - it willdecrease with time until it gets to zero at terminal velocity.

When there's air resistance, the acceleration will decrease because the force (weight - resistance) is decreasingdue to increasing resistance or friction at higher speeds.

At terminal velocity, weight = friction, so the net force is 0. Thus, the acceleration is 0. So, the speed staysconstant at terminal velocity.

Projectiles

Projectiles are free falling bodies. The vertical component of the projectile velocity is always accelerating toward the Earth at a rate of g. The vertical acceleration of g toward the Earth holds true at all times, even when the projectile is traveling up

(it's decelerating on its way up, which is the same thing as accelerating down). There is no acceleration in the horizontal component. The horizontal component of velocity is constant. What is the time the projectile is in the air? Ans: use the vertical component only- calculate the time it takes for

the projectile to hit the ground. How far did the projectile travel? Ans: first get the time in the air by the vertical component. Then use the

horizontal component's speed x time of flight. (Don't even think about over-analyzing and try to calculate theparabolic path).

When you toss something straight up and it comes down to where it started, the displacement, s, for the entiretrip is 0. Initial velocity and acceleration are opposite in sign.

When you toss something straight up and it comes down to where it started, there is symmetry. Initial velocityand final velocity are equal and opposite. Time spent going up = time spent coming down.

Orbiting in space

Satellites orbiting the Earth are in free fall. Their centripetal acceleration equals the acceleration from the Earth's gravity.

Even though they are accelerating toward the Earth, they never crash into the Earth's surface because the Earthis round (the surface curves away from the satellite at the same rate as the satellite falls).

Below are old AAMC topics that has been deprecated or changed

Units and dimensions

A unit is a label for a quantity. unit + unit = unit unit - unit = unit unit x unit = unit2

unit / unit = no unit Dimensions are powers of units. unit = one dimension. unit2 = two dimension. unit3 = three dimension.

Common SI units

Quantity SI unit Name

Length m meter

Area m2 meter squared

Volume m3 meter cubed

Mass kg kilogram

Density kg/m3 kilogram per meter cubed

Time s second

Speed m/s meter per second

Acceleration m/s2 meter per second squared

Force N Newton

Pressure Pa Pascal

Temperature K Kelvin

Energy J Joule

Power W Watt

Charge C Coulomb

Potential V Volt

Current A Ampere

Resistance Ω Ohm

Magnetic field T Tesla

The product of operations involving all SI units is also in SI units.

Prefixes for units

Prefix Abbreviation Multiplier

exa E 1018

peta P 1015

tera T 1012

giga G 109

mega M 106

kilo k 103

hecto h 102

deka da 101

deci d 10-1

centi c 10-2

milli m 10-3

micro μ 10-6

nano n 10-9

pico p 10-12

femto f 10-15

atto a 10-18

Force, Motion, and Gravitation

Center of mass

The center of mass is the average distance, weighted by mass

In a Cartesian coordinate, the center of mass is the point obtained by doing a weighted average for all thepositions by their respective masses.

The center of mass of the Earth and a chicken in space is going to be almost at the center of the Earth, becausethe chicken is tiny, and its coordinate is weighted so.

The center of mass between two chickens in space is going to be right in the middle of the two chickens,because their positions are weighted equally.

You do not have to obtain the absolute coordinates when calculating the center of mass. You can set the pointof reference anywhere and use relative coordinates.

The center of mass for a sphere is at the center of the sphere. The center of mass of a donut is at the center of the donut (the hole).

Newton's first law, inertia

The law of inertia basically states the following: without an external force acting on an object, nothing will changeabout that object in terms of speed and direction.In the absence of an external force:

Something at rest will remain at rest Something in motion will remain in motion with the same speed and direction. Objects are "inert" to changes in speed and direction.

Newton's second law (F = ma)

A net force acting on an object will cause that object to accelerate in the direction of the net force.

The unit for force is the Newton. N = kg·m/s2

Both force and acceleration are vectors because they have a direction. Many MCAT questions omit the direction attribute because it is so obvious. For example, when an apple falls to

the ground (or on Newton), we all know that the force of gravity acts downwards, and the apple of course, fallsdownwards. Questions in this scenario are just simple cases of plugging in the formula

However, more difficult questions have directional attributes associated with them. For example, when a bar ofsoap slides down an inclined plane, the force of gravity acts downwards, but the acceleration is not completelydownwards, but is "slanted". Therefore, you need to do vector analysis (simple ones only. The MCAT is too shortfor complex, time-consuming ones that appear in your physics midterm).

Newton's third law, forces equal and opposite

Every action has an equal and opposite reaction

for the MCAT, you need to know that this law applies to propulsion. This is why rockets work even in the vacuumof space.

Concept of a field

For the purposes of the MCAT, fields are lines. When lines are close together, that's shows a strong field. When lines are far apart, that shows a weak field. Lines / fields have direction too, and that means they are vectors. Things travel parallel, perpendicular, or spiral to the field line.

Law of gravitation (F = Gm1m2/r^2)

Gravity decreases with the square of the distance. If the distance increases two fold, gravity decreases by a factor of four. The "distance" is the distance from the center of mass between the two objects. Gravity is the weakest of the four universal forces. This weakness is reflected in the universal gravitational constant, G, which is orders of magnitude smaller than

the Coulomb's constant.

Uniform circular motion

Memorize the equations

acceleration:

force:

circumference:

arc:

area:

sector:

note that theta is always in radians. To convert degrees to radians, use this formula: The simple harmonic laws of frequency and period applies here also.

Get the concepts

Distinguish between velocity and speed: Velocity is displacement over time. Speed is the distance over time. Displacement is the shortest, straight-line distance between two points on the perimeter of a circle (technically,

this is called the chord). Distance is circumference and arc. Some typical cases:

o For displacements and distances that approach zero, the instantaneous velocity equals the speed.o For a quarter around the circle (pi/2 radians or 90 degrees), the displacement is the hypotenuse of a

right-angled triangle with the radius as the other two sides. Using Pythagoras, the displacement issquare root of 2r^2. The distance is the arc of 1/4 circumference.

o For half around the circle, the displacement is the diameter and the distance is the half thecircumference.

o For three quarters around the circle, the displacement is again obtained by Pythagoras. The magnitudeof the displacement here is the same as that at a quarter of a circle, but the direction is different. Thedistance, is 3/4 of the circumference.

o Complete around the circle, the displacement is zero, which makes the velocity also zero. The distance isthe circumference.

The velocity is always less or equal to the speed. The displacement is always less or equal to the distance. Displacement and velocity are vectors. Distance and speed are not. Moving around a circle at constant speed is also simple harmonic motion. frequency = how many times the object goes around the circle in one second. period = time it takes to move around the entire circle.

Centripetal Force (F=-mv2/r)

Centripetal force is due to centripetal acceleration. Centripetal acceleration is due to changes in velocity when goingaround a circle. The change in velocity is due to a constant change in direction.

Centripetal force:o Sometimes a negative sign is used for centripetal force to indicate that the direction of the force is

toward the center of circle.

Centripetal acceleration: The direction of both the acceleration and the force is toward the center of the circle. The tension force in the string (attached to the object going in circles) is the same as the centripetal force. When the centripetal force is taken away (Such as when the string snaps), the object will fly off in a path tangent

to the circle at the point of snap.

Weight

Weight is the force that acts on a mass

Weight is a force. It has a magnitude and a direction. It is a vector. Because it is a force, F=ma holds true. Your weight on the surface of the Earth: F=mg, where g is the acceleration due to Earth, which is just under 10. You weigh more on an elevator accelerating up because F=mg + ma, where a is the acceleration of the elevator. An elevator accelerating up is the same thing as an elevator decelerating on its way down, in terms of the

acceleration in F=mg + ma. You weigh less on an elevator accelerating down because F=mg - ma, where a is the acceleration of the elevator. An elevator accelerating down is the same thing as an elevator decelerating on its way up, in terms of the

acceleration in F=mg - ma. You weight less when you are further away from the Earth because the force of gravity decreases with distance. However, you are not truly "weightless" when orbiting the Earth in space. You are simply falling toward the

Earth at the same rate as your space craft. You gain weight as you fall from space to the surface of the earth. For a given mass, its weight on Earth is different from its weight on the Moon. When something is laying still on a horizontal surface, the normal force is equal and opposite to the weight. When something is laying still on an inclined plane, the normal force and friction force adds up in a vector

fashion to equal the weight.

Friction, static and kinetic

Friction is a force that is always in the direction to impede the sliding of surfaces.

Static friction: Kinetic friction:u is the coefficient of friction and N is the normal force.

Like any other force, friction is a vector. However, its direction is easy because it's always opposite to the motionof the surface involved.

Static friction pertains to objects sitting still. An object can sit still on an inclined plane because of static friction. Kinetic friction pertains to objects in motion. A key sliding across the table eventually comes to a stop because of

kinetic friction. Static friction is always larger than kinetic friction. The coefficient static friction is always larger than the coefficient of kinetic friction. The coefficient of friction is intrinsic to the material properties of the surface and the object, and is determined

empirically. The normal force at a horizontal surface is equal to the weight The normal force at an inclined plane is equal to the weight times the cosine of the incline angle (see inclined

planes). We can walk and cars can run because of friction. Lubricants reduce friction because they change surface properties and reduce the coefficient of friction. Every time there is friction, heat is produced as a by-product.

Motion on an inclined plane

Gravity is divided into two components on an inclined plane.o One component is normal (perpendicular) to the plane surface: FN = mg·cosθo The other component is parallel to the plane surface: F|| = mg·sinθ

To prevent the object from crashing through the surface of the inclined plane, the surface provides a normalforce that is equal and opposite to the normal component of gravity.

Friction acts parallel to the plane surface and opposite to the direction of motion. In a non-moving object on an inclined plane: normal component of gravity = normal force; parallel component of

gravity = static friction. Unless the object levitates or crashes through the inclined plane, the normal force always equals the normal

component of gravity. In an object going down the inclined plane at constant velocity: parallel component of gravity = kinetic friction

(yes, they're equal, don't make the mistake of thinking it's larger. Constant velocity = no acceleration = no netforce).

In an object that begins to slip on the inclined plane: parallel component of gravity > static friction. In an object that accelerates down the inclined plane: parallel component of gravity > kinetic friction.

When you push an object up an inclined plane, you need to overcome both the parallel component of gravityand friction.

When you push or pull an object up an inclined plane, make sure you divide that force into its components. Onlythe component parallel to the plane contributes to the motion.

Analysis of pulley systems

Pulleys reduce the force you need to lift an object. The catch - it increases the required pulling distance.

For the purpose of the MCAT, just memorize the simple pulley systems below. Rule of thumb: The ropes on either side of a moving pulley contributes to pulling the load. The MCAT will most probably give you simple pulleys where only the above rule is applicable. Complex pulleys will have additional ropes that contribute to the pulling of the load (most likely not tested on

the MCAT). The distance of pulling increases by the same factor that the effort decreases.

There are no moving pulleys here. If the weight of the box is 100 N, you have to pull with a force of 100 N. Forevery 1 meter you pull, the box goes up 1 meter.

When there is one moving pulley, the force needed to pull is halved because strings on both side of the pulleycontribute equally. You supply 50 N (which is transmitted to the right-hand rope) while the left-hand ropecontributes the other 50 N. Because effort here is halved, the distance required to pull the box is doubled.

There are two moving pulleys here. Counting the ropes reveal that when we tug on one rope, it getstransmitted to a system where 4 ropes pull on the load. Thus, you can pull the 100 N box with only 25 N.However, for every 4 m you pull, the box only goes up 1 m.

This is a complex pulley. Just like the simple pulleys, the ropes on both sides of the moving pulley contribute.Here, the left-most rope contributes also. This makes 3 contributing ropes, which makes the effort required tobe reduced by a factor of 3. The distance you need to pull here is 3 times the distance the box will travel.

Force

There are 4 universal four-ces... get it? Universal forces are also called fundamental forces. The four forces are:

o The strong force: also called the nuclear force. It is the strongest of all four forces, but it only acts atsubatomic distances. It binds nucleons together.

o Electromagnetic force: about one order of magnitude weaker than the strong force, but it can act atobservable distances. Binds atoms together. Allows magnets to stick to your refrigerators. It isresponsible for the fact that you are not falling through your chair right now (MCAT people love tothrow you quirky examples like this one).

o Weak force: roughly 10 orders of magnitude weaker than the strong force. Responsible for radioactivedecay.

o Gravity: roughly 50 orders of magnitude weaker than the strong force. Responsible for weight (notmass!). Also, responsible for planet orbits.

Equilibrium and Momentum

Equilibrium

When something is in equilibrium, the vector sum of all forces acting on it = 0. Another way to put it: when something is in equilibrium, it is either at rest or moving at constant velocity. Yet another way to put it: when something is in equilibrium, there is no overall acceleration.

Concept of force, units

Force makes things accelerate, change velocity or change direction. In the MCAT, a force is indicated by an arrow. The direction of the arrow is the direction of the force. The magnitude of the force is often labeled beside the arrow. F=ma, so the unit for the force is kg·m/s2

Translational equilibrium (Sum of Fi = 0)

When things are at translational equilibrium, the vector sum of all forces = 0. Things at translational equilibrium either don't move, or is moving at a constant velocity.

If an object is accelerating, it's not in equilibrium. Deceleration is acceleration in the opposite direction. At translational equilibrium:

o An apple sitting still.o A car moving at constant velocity.o A skydiver at falling at terminal velocity.

NOT at translational equilibrium:o An apple falling toward the Earth with an acceleration of g.o A car either accelerating or decelerating.o A skydiver before he or she reaches terminal velocity.

Rotational equilibrium (Sum of Torque = 0)

When things are at rotational equilibrium, there the sum of all torques = 0. Conventionally, positive torques act counterclockwise, negative torques act clockwise. When things are at rotational equilibrium, they either don't rotate or they rotate at a constant rate (angular

velocity, frequency). You cannot have rotational equilibrium if there is angular acceleration. Deceleration is acceleration in the opposite direction. At rotational equilibrium:

o Equal weights on a balance.o Propeller spinning at a fixed frequency.o Asteroid rotating at a constant pace as it drifts in space.

NOT at rotational equilibrium:o Unequal weights in a balance such that the balance is begins to tilt.o Propeller spinning faster and faster.o Propeller slowing down.

Analysis of forces acting on an object

Draw force diagram (force vectors). Split the forces into x, y and z components (normal and parallel components for inclined planes). Add up all the force components. The resulting x, y and z components make up the net force acting on the object. Use Pythagoras theorem to get the magnitude of the net force from its components. Use trigonometry to get the angles. ... more on vector components

Newton's first law, inertia

The significance of Newton's first law on equilibrium is: things in equilibrium will remain in equilibrium unlessacted on by an external force.

The significance of Newton's first law on momentum is: things resist change in momentum because of inertia(try stopping a truck. It's not easy because it resists changes to its huge momentum).

... more on Newton's first law

Torques, lever arms

Torque

oo Torque is the angular equivalent of a force - it makes things rotate, have angular acceleration, change

angular velocity and direction.o The convention is that positive torque makes things rotate anticlockwise and negative torque makes

things rotate clockwise. Lever

o The lever arm consists of a lever (rigid rod) and a fulcrum (where the center of rotation occurs).o The torque is the same at all positions of the lever arm (both on the same side and on the other side of

the fulcrum).

oo If you apply a force at a long distance from the fulcrum, you exert a greater force on a position closer to

the fulcrum.o The catch: you need to move the lever arm through a longer distance.

Weightlessness

There are two kind of weightlessness - real and apparent.o Real weightlessness: when there is no net gravitational force acting on you. Either you are so far out in

space that there's no objects around you for light-years away, or you are between two objects withequal gravitational forces that cancel each other out.

o Apparent weightlessness: this is what we "weightlessness" really means when we see astronautsorbiting in space. The astronauts are falling toward the earth due to gravitational forces (weight), butthey are falling at the same rate as their shuttle, so it appears that they are "weightless" inside theshuttle.

Momentum

Momentum = mv, where m is mass, v is velocity and the symbol for momentum is p. Impulse = Ft, where F is force and t is the time interval that the force acts.

Impulse = change in momentum: Conservation of linear momentum

o Total momentum before = total momentum after.o Momentum is a vector, so be sure to assign one direction as positive and another as negative when

adding individual momenta in calculating the total momentum.o The momentum of a bomb at rest = the vector sum of the momenta of all the shrapnel from the

explosion.o Total momentum of 2 objects before a collision = total momentum of 2 objects after a collision.

Elastic collisionso Perfectly elastic collisions: conservation of both momentum and kinetic energy.o Conservation of kinetic energy: total kinetic energy before = total kinetic energy after.o Kinetic energy is scalar, so there are no positive / negative signs to worry about.o If you drop a ball and the ball bounces back to its original height - that's a perfectly elastic collision.

o If you throw a ball at a wall and your ball bounces back with exactly the same speed as it was before ithit the wall - that's a perfectly elastic collision.

Inelastic collisionso Conservation of momentum only.o Kinetic energy is lost during an inelastic collision.o Collisions in everyday life are inelastic to varying extents.o When things stick together after a collision, it is said to be a totally inelastic collision.

Work and Energy

Work

W = Fdcosθ F is force, d is the distance over which the force is applied, and θ is the angle between the force and distance. Derived units, sign conventions

o Work is energy, and the unit is the Joule.o Joule = N·m = kg·m/s2·m = kg·m2/s2

o If the force and the distance applied is in the same direction, work is positive.o For example, pushing a crate across a rough terrain involves you doing positive work (you are pushing

forward and the crate is moving forward).o If the force and the distance applied is in opposite directions, work is negative.o For a non-rotating system, friction always does negative work because it acts against the direction of

motion.o If the force is acting in one direction, but the object moves in a perpendicular direction, then no work is

done.o The classic example is that no work is done by your arms when you carry a bucket of water for a mile.

Because you are lifting the bucket vertically while its motion is horizontal.o If you like math, then everything you need to know is already contained in the mathematical formula.

Cosine of 90 is zero; cosine of anything below 90 is positive and between 90-180 is negative ...so forth. Amount of work done in gravitational field is path-independent

o Unlike friction, gravity always acts downwards. Thus, it does not matter what detour you take becausesideward motion perpendicular to the gravitational force involves no work.

o Pushing an object at constant speed up a frictionless inclined plane involves the same amount of work asdirectly lifting the same object to the same height at constant speed.

o Sliding down a frictionless inclined plane involves the same gravitational work as doing a free fall at thesame height.

Mechanical advantageo Mechanical advantage = little input force (effort) -> large output force.o Using the lever arm can achieve mechanical advantage.o Using pulleys can achieve mechanical advantage.

Work-kinetic energy theoremo Work on an object can transform into kinetic energy.

When you pushing on an object, it will move: Fd = ½mv2

When gravity does work on an object, it will move: Fweighth = mgh = ½mv2

o Kinetic energy of an object can do work. A moving object can slide up an inclined plane before coming to a stop: ½mv2 = mgh A moving object can slide against friction for a while before coming to a stop: ½mv2 = Ffrictiond

Powero Power is the rate of work, or work over time: P = W/to The unit for power is the Watt, or W (don't confuse this W with the shorthand of work).o Watt = Joule / second

Energy

Work and energy are interchangeable. All types of energy have the same unit - the Joule. Kinetic energy: KE = 1/2 mv^2; units

o KE = ½mv2

o Unit = Joule = kg·m2/s2

o At the same speed, the larger mass has the larger kinetic energy.o When you double the mass, you double the kinetic energy.o At the same mass, the higher speed has the larger kinetic energy.o When you double the speed, you quadruple the kinetic energy.o Speed is more important than mass for the kinetic energy because speed is squared.

Potential energyo PE = mgh (gravitational, local)

PE = mgh is local because it only works on the surface of the Earth. h is the distance from the Earth's surface. PE = mgh is derived from a more general formula - see below. On earth, g is 9.8. g is larger for planets with a higher mass to radius ratio.

o PE = 1/2kx^2 (spring) x is distance of the end of the spring from its equilibrium position. k is the spring constant. Stiff springs have a larger k because they are harder to stretch (it takes more energy to stretch

them).o PE = -GmM/r (gravitational, general)

This is the general formula for gravitational potential energy. r is the distance between the center of the two attracting objects. G is the universal gravitation constant - it is the same for everything. m and M are the mass of the two attracting objects.

Conservation of energyo The total amount of energy before = the total amount of energy after.o Gravitational potential energy is converted to kinetic energy as an object falls, but the total amount of

energy stays the same.o Kinetic energy is converted to heat and sound energy as a crate slides to a stop on a rough surface.

Conservative forceso If a force doesn't dissipate heat, sound or light, then it is a conservative force.o Work done by conservative forces are path independent.o Conservative forces are associated with a potential energy.o For example, the force from a spring can be stored as spring potential energy.o Gravitational force can be stored as gravitational potential energy.o Electromagnetic forces are also conservative.o non-conservative include frictional forces and human exertion. When friction acts on an object, the heat

and sound released cannot be recovered. When you flex your arm, you lose heat that cannot berecovered (you cannot re-absorb the heat you lost).

Power, unitso Power is the rate of energy use.o The unit for power is the Watt, or Joule per second.o Lifting a crate in one minute requires more power than lifting the same crate in an hour.

Waves and Periodic Motion

Periodic motion

Amplitude, period, frequency

oo Amplitude (A): how high the peaks are or how low the troughs are, in meters.

The displacement is how far the wave vibrates / oscillates about its equilibrium (center)position.

The amplitude is the maximum displacement. Amplitude is correlated with the total energy of the system in periodic motion. Larger

amplitude = greater energy.o Period (T): the time it takes for one cycle, in seconds.

T = 1/fo Frequency (f): the rate, or how many cycles per second, in Hertz (cycles per second).

f = 1/T Sometimes, frequency is in rpm (revolutions per minute). rpm = cycles per second x 60.

o Angular frequency (w): the rate, in how many radians per second. w = 2πf w is also called angular velocity.

Phase

o

o In phase: the waves are 0 or 2π radians (0 or 360°) apart. The resulting amplitude (sum of thewaves) is twice the original.

o Completely out of phase: the waves are π radians (180°) apart. The resulting amplitude is zero.o Out of phase: resulting amplitude is between 0 and twice the original.

Hooke's law, force F= -kxo F is the force that acts to restore the spring back to its equilibrium position, or restoring force.o k is the spring constant. Stiffer springs have a higher k value.o x is the displacement. The amplitude (A) is the maximum x value.o Potential energy = PE = ½kx2

o Kinetic energy = KE = ½mv2

o At the equilibrium position x = 0, PE = 0, KE = maximum.o At the maximum displacement (amplitude) x = A, PE = maximum, KE = 0.o At any point, PE + KE = maximum PE = maximum KE = constant.o constant = PEmax = ½kA2

o constant = KEmax = ½mv2 at x = 0 Simple harmonic motion; displacement as a sinusoidal function of time

o x = A·sin(wt)o x is displacement.o A is amplitude.o w is angular frequency (also called angular velocity).o t is time.o Examples of simple harmonic motion

Oscillating spring. Pendulum. Things going around a circle at constant speed (when plot the x axis position against

time). Motion of a spring with mass attached to its end

oo T is period, m is the mass of the attached mass, and k is the spring constant.

o A simpler way to express this is:o w is the angular frequency. The spring vibrates faster if it's stiffer and if the mass attached to it

is smaller. Motion of a pendulum

oo T is period, L is the length of the string, and g is 9.8.

o A simpler way to express this is:o w is the angular frequency. The pendulum oscillates faster when gravity is large and when the

string is short. General periodic motion: velocity, amplitude

o At the equilibrium position, PE = 0, KE = maximum.o At the maximum displacement (amplitude) x = A, PE = maximum, KE = 0.o At any point, PE + KE = maximum PE = maximum KE = constant.

o constant = PEmax

= ½kA2 for a spring. = mgA for a pendulum, where A is the maximum height that the pendulum can gain

during a swing.o constant = KEmax = ½mv2 at the equilibrium position.o If you are given the velocity at the equilibrium position, then you should be able to find out the

amplitude by setting maximum KE = maximum PE.o If you are given the amplitude, then you should be able to find out the velocity at the

equilibrium position by setting maximum PE = maximum KE.

Wave Characteristics

Transverse and longitudinal waveso Transverse wave: wave displacement is perpendicular to the direction of motion.

Light. Electromagnetic radiation. A standing wave by oscillating a string side ways. The speed for such a wave = square

root of (string tension / mass per unit length of the string). For the MCAT, just know thattense, light strings can produce faster transverse waves.

o Longitudinal wave: wave displacement is parallel to the direction of motion. Sound. Pressure wave. Earth quakes.

Wavelength, frequency, velocityo v = fλo v is velocity, f is frequency, and λ is wavelength.o Some times, frequency is also written as ν.o Wavelength is in meters, frequency is in Hertz and velocity is in meters per second.

Amplitude, intensityo Amplitude is correlated with the energy of the wave. Greater amplitude = greater energy of the

wave.o Intensity = energy per area per time = power per area.o Thus, amplitude and intensity are correlated. Greater amplitude leads to higher intensity.o Special note on electromagnetic waves: amplitude and intensity increases the overall energy of

electromagnetic waves such as light. However, neither amplitude nor intensity changes theenergy per photon. Energy per photon depends on wavelength. The shorter the wavelength(also the higher the frequency), the greater the energy.

Supposition of waves, interference, addition

o

oo When waves superimpose on each other, they interfere.o Interference results from the addition of waves.o When in phase waves add, the resulting wave has a greater amplitude.o When out of phase waves add, the resulting wave has a smaller amplitude.o Constructive interference: addition of waves resulting in greater amplitude.o Destructive interference: addition (cancellation) of waves resulting in diminished amplitude.

Resonanceo Resonance is when things oscillate at its maximum amplitude.o Resonance occurs at resonance frequencies.

Resonance frequencies

o Examples of standing waves and the resonance frequencies that produce them

o Frequencies can be obtained by f = v/λo Both strings and tubes open at both ends have L = n/2λo Tubes with a closed end have L = n_odd/4λo L is the length of the string/tube

Standing waves, nodeso Standing waves vibrate at resonance frequencies.o Standing waves do not propagate like other waves (that's why they're called standing waves).o Node: point where there's no oscillation.o Antinode: point where there's maximum oscillation.

Beat frequencieso Beats occur when two waves coexist at different frequencies.o The beat frequency is the difference between the frequencies of the two waves.

Refraction and diffraction

oo Refraction is the bending of waves when it meets a boundary between one medium to another.

Snell's law: n1sinθ1 = n2sinθ2 , where n is the refractive index and θ is the angle to thenormal.

When light moves to a denser medium (higher refractive index), it bends toward thenormal.

Dispersion, the bending of light through a prism, is a special case of refraction thatseparates the colors of light into a rainbow.

Rainbows are created by refraction by water droplets.

o Diffraction is the spreading (diffusion) of waves around edges of apertures and obstacles. You can hear sounds from the other side of a building because sound spreads. Shining light through a hole will not produce a dot of light, instead, it is a diffuse circle. Diffraction is the basis for the single and double slit interference experiments with light. When you think of diffraction, think "diffuse".

Sound

Production of sound

Sound is produced by vibrations in a medium. Sound can not be produced in a vacuum, nor can sound travel across a vacuum. Vibrations whose frequency is too low to hear is called infrasound. Vibrations whose frequency too high to hear is called ultrasound. Vibrations produce pressure waves that oscilate parallel to the direction of propagation. Sound is a longitudinal wave.

Relative speed of sound in solids, liquids and gases

Speed of sound in solids > liquids > gases.o The reason why sound travels the fastest in solids is because solids are the most stiff.

With all else being equal...o Speed of sound in stiff objects > elastic objects.o Speed of sound in less dense objects > more dense objects. Even though gases are less dense

than solids, sound still travels slower in them because they are too elastic.o Speed of sound in hot objects > cold objects.

Intensity of sound (decibel units, log scale)

β = 10 logI/I0

β is sound level in decibels. I is intensity. I0 is 10-12 W/m2

Intensity is power per area, or the rate of energy expenditure per area. The unit is W/m2

Intensity DecibelsI0 010 I0 10100 I0 201000 I0 30

The decibel system is based on human perception. The decibel value for sound with an intensity of I0 iszero - below this intensity, sound is not audible. As intensity increases, our perception of its loudnessonly increases to a much lesser degree.

Attenuation

Sound attenuation is the gradual loss of intensity as sound travels through a medium. Sound attenuation is the greatest for soft, elastic, viscous, less dense material.

Doppler effect (moving sound source or observer, reflection of soundfrom a moving object)

Situations where the observed frequency is higher than the actual:o Source moving toward stationary observer: fo = fs

v/v - vs

o Observer moving toward stationary source: fo = fsv + v

o/v

o Source and observer both moving toward each other: fo = fsv + v

o/v - vs

Situations where the observed frequency is lower than the actual:o Source moving away from stationary observer: fo = fs

v/v + vs

o Observer moving away from stationary source: fo = fsv - v

o/v

o Source and observer both moving away from each other: fo = fsv - v

o/v + vs

Situations where the observed frequency could be either higher or lower than the actual:o Source moving toward the observer, but the observer is moving away from the source: fo = fs

v -

vo/v - vs

o Source moving away from observer, but the observer is moving toward the source: fo = fsv + v

o/v

+ vs

fo is observed frequency. fs is actual frequency emitted by the source. v is the speed of sound. vo is thespeed at which the observer is travelling. vs is the speed at which the source is travelling.

Pitch

Pitch is the human perception of the frequency of sound. Higher frequency = higher pitch.

Resonance in pipes and strings

Frequencies can be obtained by f = v/λ Both strings and pipes open at both ends have L = n/2λ Pipes with a closed end have L = (2n-1)/4λ

Harmonics

The fundamental frequency is called the first harmonic (n = 1). The next-up frequency is called the second harmonic (n = 2).

Ultrasound

Sound has 3 fundamental properties: reflection, refraction, and diffraction. Ultrasound imaging is based on the reflection property of sound. A source emits ultrasound, which reflects off a surface back into the detector to form an image. Ultrasound is sound that is too high in frequency for humans to hear.

Fluids and Solids

Fluids

Liquids and gases are fluids. Density, specific gravity

o Density: ρ=m/V, where ρ is density, m is mass, and V is volume.o The density of water is ρwater = 1 g/mL = 1 g/cm3 = 1 kg/L.o Specific gravity is the density of something compared to water.o Specific gravity = ρ/ρwater.o The specific gravity of water is 1.

Buoyancy, Archimedes' principle

oo Archimedes' principle: buoyant force on an object = weight of the fluid displaced by the object.o FB = weightdisplaced = mdisplacedg =ρfluidVsubmergedgo The volume of an object that is submerged = the volume of fluid displaced by the object.o Things float when FB = Weight.o Things will rise upward when FB > Weight.o Things will sink when FB < Weight.

Hydrostatic pressureo Pascal's law: if you apply pressure on a liquid, the pressure is transmitted equally to all parts of

the liquid.

F1/A1 =F2/A2

The pressure input at one end is the same as the pressure output at the other. You apply a small force over a small area, and the output force at the end with the

larger area will be greater. A1d1=A2d2, where d is the distance that the end moves. The work done on one end is the same as the work output at the other.

o P = pgh (pressure vs. depth) P=ρgh P is pressure, ρ is the density of the fluid; g is the gravitational constant, h is the height

from the surface, or depth that the object is submerged. Pressure at the surface is 0 because h = 0. Pressure at a depth of h is ρgh. ρgh is the gauge pressure because it ignores the atmospheric pressure above the fluid. Absolute pressure of something submerged in the ocean = ρgh + atmospheric pressure.

Viscosity: Poiseuille flowo When a viscous fluid flows through a pipe, the flow has a front that is shaped like a parabola

bulging outward. Continuity equation (A·v = constant)

o The volume flow rate of a fluid is constant.o dV/dt = constant, where dV/dt is volume flow rate.o dV = A·dLo A·dL/dt = A·v = constant, where v is linear flow rate (velocity).

Concept of turbulence at high velocitieso Low velocity -> laminar flow.o High velocity -> turbulent flow, forms eddies.

Surface tensiono Surface tension gives the surface of a liquid the ability to support things that are very light.o For example, insects can walk on water due to surface tension.o Surface tension is due to the attraction between the molecules of the solvent.

Bernoulli's equationo P + ½ρv2 + ρgh = constant

Solids

Density: ρ=m/V, where m is mass and V is volume. Elastic properties (elementary properties)

oo Stress: the pressure exerted on an object. σ = stress = F/A.o Strain: the deformation of the object in the direction of the applied force divided by the original

length. ε = strain = ΔL/L0.o Young's modulus = stress / strain.o Young's modulus, the ratio between stress and strain, is constant until you reach the elastic

limit, where things get permanently deformed.

Elastic limit: The maximum stress something can handle before it breaks or become permanentlydeformed.

Thermal expansion coefficiento Things expand when temperature rises, and contracts with temperature falls.o ΔL = αL0ΔTo ΔL is the change in length, L0 is the initial length, ΔT is the change in temperature, and α is the

coefficient of linear expansion.o In the same fashion as linear expansion, the equations for volume and area expansions are

below.o ΔV = βV0ΔTo ΔA = γA0ΔT

Shear

oo Shear = stress / shear ratio.o Shear ratio = ΔL/L0.o When ΔL is very small compared to L0, Shear ratio is approximately the same as the shear angle.o Shear angle = tan-1ΔL/L.o Note: ΔL and L are perpendicular to each other.

Compression: solids and liquids are generally not compressible. Gasses are compressible.

Electrostatics and Electromagnetism

Electrostatics

Charge, conductors, charge conservationo Charges are either positive or negative. Zero charge is neutral.o Like charges repel, unlike charges attract.o Charge is quantized, and the unit of charge is the Coulomb.o Conductors are materials in which charges can move freely. Metals are good conductors.o Charge is always conserved. You can't create or destroy charge, you can only transfer charge from one

source to another. Insulators

o Insulators are materials in which charges can not move freely. Nonmetals are good insulators. Coulomb's law (F = kq1q2/r2, sign conventions)

o F = kq1q2/r2

o k = 9E9 Nm2/C2

o q is positive for positive charges and negative for negative charges.o Positive F = repelling force.o Negative F = attractive force.

Electric fieldo field lines

Electric field is denoted by the vector E. Lines that are closer together denote stronger fields than lines that are farther apart.

Electric fields come out of positive charges, and goes into negative charges. The unit for electric field is N/C, or Newtons per Coulomb.

o field due to charge distribution

Field lines come out of the positive end and goes into the negative end of a dipole.

Field lines for two negative charges are the same as those for two positive charges except that

the direction of the field lines would be reversed.

The direction and magitude of the field at any point in space can be calculated as the vector sum

of all the field components there.

Electric field in between a capacitor is uniform until it reaches the ends of the capacitor.

Electric field for wires runs radially perpendicular to the wire.

Electric field for a cylinder runs radially perpendicular to the cylinder, and is zero inside the

cylinder. Potential difference, absolute potential at point in space

oo Absolute potential (V) is the amount of energy per charge that something possesses.

V = U/q0 = kq/r

V is the electric potential (absolute potential) caused by q, which is experienced by q0. q is the charge that is causing the potential, not the charge that's experiencing the potential. Traditionally, q0 is the charge experiencing the potential. The magnitude of q0 is very small. U is the electrical potential energy possessed by q0. r is the distance between the potential-causing charge and the charge that's experiencing the

potential (r is always positive). if there are multiple charges contributing to the potential, then calculate the potentials each of

them causes (positive charges cause positive potentials, and negative charges cause negativepotentials), and sum them together.

The unit for potential is Volts (V) or Joules per Coulomb (J/C).o Potential difference (ΔV) is the difference between two potentials.

ΔV = VB - VA

Potential difference is used in scenarios such as the difference in potential between the twoplates of a capacitor, or the positive and negative terminals of a battery.

Equipotential lines

oo Equipotential lines are places where the potential is the same.o Equipotential lines are always perpendicular to electric field lines.

Electric dipoleo definition of dipole

dipole = a positive charge and a negative charge separated by some distance.o behavior in electric field

A dipole in an electric field will want to align itself with the electric field, such that the positive

end of the dipole is in the direction of the electric field.o potential due to dipole

To calculate the exact potential at a given point, just calculate the individual potential due to thepositive charge and the negative charge, then add them together.

Electrostatic induction

oo Induction does not involve any type of conduction.o Electrostatic induction is where a charged object induces the movement / redistribution of charges in

another object.o The classical example of electrostatic induction is picking up pieces of paper using a comb rubbed

against fur.o It's called electrostatic induction because it's static - the charged species polarizes non-charged species

by simply being there. This is not the same as electromagnetic induction, which is how electricgenerators work. Luckily electromagnetic induction is not listed as an official AAMC topic.

Gauss' lawo ΦE = EA cosθ

ΦE is electric flux. E is electric field, A is area that the field goes through, and θ is the angle between the field and

the normal of the area.o ΦE = q/ε0

For an enclosed surface, the electric flux is equal to q, the charge inside the enclosure, over thepermitivity of free space.

The net electric flux through any enclosed surface is totally dependent on the charge inside. Ifthere's no charge inside, then the net electric flux through the enclosure is zero.

o An important application of Gauss's law is the Faraday cage. Basically, the electric field inside a closedconducting cage is zero. This is because the charges on the conducting cage will rearrange to cancel outany external field.

Magnetism

Definition of the magnetic field Bo Magnetic field B exists in a region of space if a moving charge experiences a force due to its motion in

that region.o The unit for magnetic field is the Tesla (T) or N·s/m·C

Existence and direction of force on charge moving in magnetic field

oo F = qvB sinθ

o θ is the angle between the charge velocity and the magnetic field. Sometimes the sinθ is omitted as θ isassumed to be 90°.

o The force is always perpendicular to both the magnetic field and to the velocity of the charge.o You can use the right hand rule to predict the direction of the force. The thumb is the direction of a

positive charge, the middle finger is the direction of the magnetic field, and the palm faces the directionof the force.

o Special scenarios / cases Charge moving in a circle

F = qvB = mv2/r You are setting the electromagnetic force equal to the centripetal force, which

maintains the orbit. Using this equation, you can solve for whatever the question asksyou.

Current carrying wires F = qvB sinθ = (it)vB sinθ = (it)(L/t)B sinθ = iLB sinθ i is current, L is length of wire. Consider the current in the wire as moving positive charges (by tradition, the direction

of the current is defined as the direction of moving positive charges). You can calculate the direction of the force on the wire in the same way using the right

hand rule. Just treat the direction of the current the same as the direction of velocity ofa positive charge.

Two wires will attract each other if the current is in the same direction. Two wires will repel each other if the current is in opposite directions.

Electromagnetic Radiation (Light)

Properties of electromagnetic radiation (general properties only)o radiation velocity equals constant c, in vacuo

Electromagnetic radiation travels fastest in a vacuum, at a velocity equals c, or 3x108m/s Light slows down when it travels in a medium other than in vacuo. n = c/v, where n is the index of refraction for the medium, and v is the speed of light travelling in

that medium.o radiation consists of oscillating electric and magnetic fields that are mutually perpendicular to each

other and to the propagation direction

Classification of electromagnetic spectrum (radio, infrared, UV, X-rays, etc.)

o

Lower frequency, longer wavelength, less energy

Radio Causes electronic oscillations in the antenna

Microwave Causes molecular rotation

Infrared Causes molecular vibration

VisibleCan excite electrons to orbits of higher energy. Visible light ranges from 400-700 nm. 400ishbeing violet, 700ish being red.

UltravioletCan break bonds and excite electrons so much as to eject them, which is why UV isconsidered ionizing radiation.

X-rays Ionizing radiation, photoelectric effect

Gammarays

Even more energetic than X-rays

Higher frequency, shorter wavelength, more energy

Old AAMC Topics: the topics below have either been removed or modified from the official AAMC outline.

Magnetism

Orbits of charged particles moving in magnetic field

oo Perfect orbit occurs when qvB = mv2/ro When qvB < mv2/r, there isn't enough centripetal force, and the charged particle flies out of orbit.o When qvB > mv2/r, there's too much centripetal force, and the charged particle spirals inward.

General concepts of sources of the magnetic fieldo Anything that involves a moving charge creates a magnetic field

Moving charges. Current carrying wire. Solenoids and toroids. The Earth (electric current in the liquid core).

o Atoms with unpaired electrons is the other source of magnetic fields. This is basically the same deal asmoving charges, since the unpaired electrons orbiting the nuclei is the same thing as moving charges.

Magnets. Individual atoms of Ferromagnetic and Paramagnetic create magnetic fields because they have

unpaired electrons. Ferromagnetic materials have domains of aligned atoms that make themeven more susceptible to be magnetized. Both Ferro and paramagnetic material are attracted tomagnetic fields.

Diamagnetic atoms don't create magnetic fields because the electrons are paired, so theirindividual fields cancel out. Diamagnetic fields actually is repeled by an external magnetic field.

Nature of solenoid, toroid

oo Solenoid

The solenoid is just a coil of current-carrying wire. B = μ0nI. n is the number of loops per meter. I is current. The magnetic field produced by a solenoid is directly proportional to the number of coils, and to

the current.o Toroid

Toroid is just a solenoid in a circle. B = μ0NI/circumference N is the total number of loops, I is the current. More loops, smaller circle → greater magnec fiel d.

Ampere's law for magnetic field induced by current in straight wire and other simple configurationso Ampere's law lets you calculate the magnetic field at a radius r from a current-carrying wire: B = μ

0I/2πr

Comparison of E and B relationso force of B on a current

F = qvB sinθ = (it)vB sinθ = (it)(L/t)B sinθ = iLB sinθ i is current, L is length of wire. Consider the current in the wire as moving positive charges (by tradition, the direction of the

current is defined as the direction of moving positive charges). You can calculate the direction of the force on the wire in the same way using the right hand

rule. Just treat the direction of the current the same as the direction of velocity of a positivecharge.

Two wires will attract each other if the current is in the same direction. Two wires will repel each other if the current is in opposite directions.

o energy Oscilations of electric and magnetic fields (electromagnetic radiation) has energy. E = hν E is energy per photon, h is Planck's constant, and ν is the frequency of the electromagnetic

wave.

Electronic Circuit Elements

Circuit elements

Current (I = ΔQ/Δt, sign conventions, units)

o

o Current is the rate of charge flow through the cross-section of a conductor (wire).o Traditionally, the direction of current is taken as the flow of positive charges.o The unit for current is Coulombs per second, C/s.

Battery, electromotive force, voltageo Electromotive force (emf) is really not a force, but a potential difference, with the unit voltage.o A battery is a source of emf.o If the battery has no internal resistance, then potential difference across the battery = EMF.o If the battery has internal resistance, then potential difference across battery = EMF - voltage

drop due to internal resistance. Terminal potential, internal resistance of battery

oo Terminal potential is the voltage across the terminals of a battery.o Internal resistance of a battery is like a resistor right next to the battery connected in series.o Terminal potential = EMF - IRinternal

Resistanceo Ohm's law (I = V/R)o resistors in series

Iseries = I1 = I2 = I3

All resistors in series share the same current. Vseries = V1 + V2 + V3

Voltage drop among resistors in series is split according to the resistance - greaterresistance, greater voltage drop (V = IR).

o resistors in parallel

Vparallel = V1 = V2 = V3

All resistors in parallel share the same voltage. Iparallel = I1 + I2 + I3

Current among resistors in parallel is split according to the resistance - greaterresistance, less current (I = V/R).

o resistivity (ρ = RA/L) Resistivity is the inverse of conductivity. Greater resistivity, greater resistance of the material. Rearranging the above equation to get R = ρL/A. To make a wire of low resistance, select

a material that has low resistivity, keep the wire short, and keep the diameter of thewire large.

Extension cords are made really thick to keep the resistance down, so it doesn't heat upand cause a fire.

Capacitanceo concept of parallel-plate capacitor

C = Q/V = εA/d Greater capacitance is created by a greater charge on plates (Q) for a given voltage (V),

greater plate area (A), or smaller distance between plates (d). V = Ed, where V is voltage across capacitor, E is electric field between capacitor, and d is

the distance between capacitor plates.o energy of charged capacitor

U = Q2/2C = ½QΔV = ½C(ΔV)2

U is the potential energy of the charged capacitor, Q is charge stored (magnitude ofeither +Q or -Q on one of the plates), C is capacitance.

o capacitors in series

1/Ceq = 1/C1 + 1/C2 + 1/C3

o capacitors in parallel

Ceq = C1 + C2 + C3

o dielectric Dielectric = nonconducting material. Inserting a dielectric between the plates of a capacitor increases the capacitance by

either increasing Q (if V is constant) or decreasing V (if Q is constant). V = V0/κ C = κC0

Discharge of a capacitor through a resistoro Charge

o Discharge

o During the discharge of a capacitor, the capacitor acts as a battery and drives current flow,which decreases with time as the capacitor discharges.

Conductivity theoryo Conductivity is affected by electrolyte concentration:

No electrolyte, no ionization, no conductivity. Optimal concentration of electrolyte, greatest conductivity due to greatest mobility of

ions. Too much electrolyte, ions are too crowded, less ion mobility, less conductivity.

o Conductivity is affected by temperature: In metals, conductivity decreases as temperature increases. In semiconductors, conductivity increases as temperature increases. At extremely low temperatures (below a certain critical temperature typically a few

degrees above absolute zero), some materials have superconductivity - virtually noresistance to current flow, a current will loop almost forever under such conditions.

o Conductivity (σ) is the inverse of resistivity (ρ).o Place a capacitor inside a solution, the solution will conduct a current between the plates of the

capacitor, thus you can measure the conductivity of a solution using a capacitor.

Circuits

Power in circuits (P = VI, P = I2R)o P = IV = I2Ro P is power, I is current, V is voltage, R is resistance.o Power companies try to save the amount of copper needed for power lines by using thinner

wires, which makes R quite high.o To minimize P dissipated by the wires, they minimize I by maximizing V. This is why power lines

transfer electricity at high voltage.

Alternating Currents and Reactive Circuits

Root-mean-square currento Irms = I

max/√2 = 0.7 Imax

Root-mean-square voltageo Vrms = V

max/√2 = 0.7 Vmax

Vrms = IrmsR Pavg = IrmsVrms = I2

rmsR

Light and Geometrical Optics

Light (Electromagnetic Radiation)

Concept of interference, Young double slit experimento Review basic interference concepts hereo In order for interference to occur, the follow conditions must hold:

the interfering light sources must be coherent. This means they must constantly maintain thesame phase relationship. The light coming from the two slits in Young's double slit experimentare coherent because a single light source shines through both slits.

the light source must be monochromatic (of single color/wavelength).

o dsinθ = mλ bright bands occur at m = 0, +/-1, +/-2 ...etc dark bands occur at m = +/-0.5, +/-1.5, +/-2.5 ...etc

Thin films, diffraction grating, single slit diffractiono Thin films provide a means for interference to occur.

Light reflecting off the outer and inner boundary of a thin film interfere with each other. A film of oil on water has the appearance of a swirly rainbow due to this interference.

oo Diffraction grating

Diffraction = light spreads out after passing through the slit, instead of going in a straight path. Diffraction grating = a slab with many slits close together. The equation for a diffraction grating is the same as the double-slit experiment. dsinθ = mλ d is the distance between the slits, everything else is the same as the double-slit experiment. bright bands occur at m = 0, +/-1, +/-2 ...etc

dark bands occur at m = +/-0.5, +/-1.5, +/-2.5 ...etco Single slit

Light shining through a single slit casts a central bright band followed by a series of maximas andminimas on either side.

The equation for a single slit diffraction is different from the equation for the double slit. asinθ = mλ a is the width of the slit. Maxima occurs for m = 0 (big central maxima), +/-1.5, +/-2.5 , etc. Minima occurs for m = +/-1, +/-2, +/-3, etc.

Other diffraction phenomena, X-ray diffractiono Light shining through a pin hole will not appear on the screen as a pin hole. Instead, it will be a

diffraction pattern of circular bright and dark bands, with a central bright band.o Light shining past an opaque boundary will not cast a sharp shadow of the boundary on the screen.

Instead, fringes of bright and dark bands appear above the boundary.o Light shining past a penny will not cast a completely black shadow. Instead, there will be a central bright

spot, as well as patterns of bright and dark rings.o X-ray diffraction = X-rays diffracting on a crystal. Patterns of interference that results from this is used to

deduce the structure of the molecules in the crystal. Polarization of light

o Unpolarized light = light with electric field oscilating in many planes.o Polarized light = light with electric field oscilating in only one plane.o Applications of polarization:

Selective absorption: pass light through polarizer that absorbs all but light with electric field inone plane.

Reflection: at a certain polarizing angle, all reflected light is polarized. Double refraction: birefringent materials have two indices of refraction that splits the incident

light into two rays polarized perpendicular to each other. Scattering: air molecules scatter light, which becomes polarized. Opticaly active molecules either rotate polarized light clockwise or counterclockwise.

Doppler effect (moving light source or observer)o Red shift = frequency decreases = occurs when source and observer is moving away from each other.o Blue shift = frequency increases = occurs when source and observer is moving toward each other.o Observed in astronomy, when stars appear redder/bluer than they really are because they are moving

away/toward us.o The equation for the doppler effect for light is the same as the doppler effect for sound, except instead

of using speed of sound v, you now use the speed of light c. For red shift, use the equation for sourcemoving away from observer. For blue shift, use the equation for source moving toward observer.

Visual spectrum, coloro energy

Blue = greatest energy, shortest wavelength, highest frequency. Red = least energy, longest wavelength, lowest frequency. Energy per photon = hν, where h is plank's constant and ν is frequency.

o lasers Laser = light amplification by stimulated emission of radiation. Normal light emission = spontaneous emission. Laser emission = stimulated emission. Repeated stimulated emission inside the lasing medium (by reflecting light back and forth

through it) amplifies light.

Geometrical Optics

Reflection from plane surface (angle of incidence equals angle of reflection)

oo mirrors completely reflect light.o going from one medium to another results in partial reflection of light.

Refraction, refractive index n, Snell's law (n1sinθ1 = n2sinθ2)

Dispersion (change of index of refraction with wavelength)o blue light refracts more than red light in a prism.o white light passes through a prism and gets split into colors of the rainbow due to dispersion.

Conditions for total internal reflectiono Going from a medium of high index of refraction to a medium of low index of refraction.o Angle of incidence > critical angle.o Find the critical angle by: n1sinθc = n2sin90°

n1 > n2

θc = critical angle Spherical mirrors

o Image height vs. Object distance:

note: this curve only shows the height of the image, not the position.

onote: this curve only shows the height of the image, not the position.

o mirror curvature, radius, focal length mirror curvature can be concave or convex. concave mirrors can focus light, so it's converging. convex mirrors can't focus light, so it's diverging. The focal length is 1/2 of the radius of curvature. converging mirrors have positive focal length, while diverging mirrors have negative focal

length. It's called the focal length because rays parallel to the principle axis of the mirror will converge

at the focal point (for diverging mirrors, the extrapolated rays will pass through the focal point).o use of formula (1/p) + (1/q) = 1/f with sign conventions

For the purpose of the MCAT, p is always positive unless the MCAT explicitly tells you otherwise. q is positive if the image is real. For mirrors, this is when the image is in front of the mirror. For

lenses, this is when the image is behind the lens. f is positive when the mirror/lens is converging. For mirrors, this is when the mirror is concave.

For lenses, this is when the lens is convex. M = h'/h = -q/p, where M is magnification, h' is height of image, h is height of object.

o real and virtual images real images are always inverted, and can be cast on a screen. virtual images are always erect (noninverted), and can not be cast on a screen. For concave mirrors, real images (positive q) are formed in front of the mirror, where light is

reflected by the mirror and can be cast on a screen. It's impossible for light to be cast behind themirror, so anything behind the mirror is virtual (negative q).

For convex mirrors, images are always virtual (negative q). Note: diverging mirrors and lenses (convex mirrors and concave lenses) can never form real

images. Thin lenses

o You don't have to re-learn everything for lenses, because they are almost the same as mirrors:o Convex lenses are the same as concave mirrors (both are converging) except for the following:

Real images are on the opposite side of the lens as the object. Because light travels through thelens and can focus on a screen behind the lens.

Virtual images are on the same side of the lens as the object. Because light can't focus in front ofa lens and be cast on a screen.

o Concave lenses are the same as convex mirrors (both are diverging) except for the following: The virtual images formed by the lens is on the same side of the lens as the object. Because light

can't focus in front of a lens and be cast on a screen.o The image height vs. object distance curve is exactly the same as those of mirrors (convex lenses the

same as concave mirrors, concave lenses the same as convex mirrors). Refer to above.o converging and diverging lenses, focal length

Focal length for converging lens is positive. Converging lens is convex. Focal length for diverging lens is negative. Diverging lens is concave.

o use of formula (1/p) + (1/q) = 1/f, with sign conventions same deal as with mirrors. p always positive. q positive if real, and negative if virtual. f positive if converging, and negative if diverging.

o real and virtual images Real images are inverted and can be cast on a screen. Virtual images are erect and can not be cast on a screen. For convex lenses, real images (positve q) are formed behind the lens because light passes

through the lens and focuses there. For concave lenses, images are always virtual (negative q), and forms in front of the lens.

o lens strength, diopters Lens strength, or lens power is measured in diopters. P = 1/f where P is in diopters.

o lens aberration spherical aberrations: not all light will focus at the focal point. chromatic abberation: blue light gets refracted more than red light, so different colors focus

differently. Combination of lenses

o The real image formed by a lens can be used as the object for another lens.o Magnification by multiple lenses is the product of all the individual magnifications.

Ray tracing

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o For mirrors:1. First draw a parallel line from the object, as it bounces off the mirror, it intersects the focal

point. Now, which focal point to intersect? The left or right? Use common sense: for concavemirrors, it's going to focus the ray to the left focal point. For convex mirrors, which can't focus,it's going to diverge the ray, which means you're going to have to extrapolate it to the right focalpoint.

2. Next draw a line that intersects the R point on the principle axis. Which R? Left or right? Should Iextrapolate? Again, use common sense: The ray drawn should bounce right back its originalpath, and not be reflected else where. By eye-balling the mirror, you should be able to figurethis out.

3. Now, you already have two rays drawn, and that is enough to make an intersection. Use thisintersection as a guide to drawing the last ray. The last ray should first intersect the focal point,then bounce off the mirror parallel to the principle axis. Which focal point to intersect? Should Iextrapolate? There's only one combination for the ray here to fit the intersection already madeby the previous two rays. The trick to do this is to draw the parallel line first, and force it tointersect the intersection already made by the previous two rays.

For lenses (similar to the way you draw rays for mirrors):0. First draw the parallel → focal point ray. It should make sense which focal point the ray should

hit/extrapolate given the converging/diverging nature of the lens.1. Next draw a ray intersecting the center of the lens.2. Lastly, using the intersection already made by the previous two rays as a guide, draw the focal

point → parallel ray. Again, draw the parallel line first and force it to intersect the interseconalready made by the previous two rays.

Optical instrumentsEye = lens focuses real image on retina.Glasses = diverging (concave) lens for near-sightedness, converging (convex) for far-sightedness.Magnifying glass = virtual, erect, larger image formed when p < f for a converging lens.

Atomic and Nuclear Structure (Physics Portion)

Atomic Structure and Spectra

Emission spectrum of hydrogen (Bohr model)

Bohr model:o An electron orbits the positively charged nucleus in the same way that the earth orbits the Sun.o Electrostatic attraction pulls the electron toward the nucleus.o The electron orbits a high speed to prevent it from crashing into the nucleus.o The electron can orbit at different energy levels: n=1, n=2, n=3 ...etc.o The higher the energy level, the larger the radius from the nucleus.

Emission spectrum of hydrogen:o When an electron transitions from a higher energy level to a lower energy level, it emits

electromagnetic radiation.o The emission spectrum of hydrogen consists of sharp, distinct lines.

Atomic energy levels

quantized energy levels for electronso The distinct lines of the emission spectrum prove that electron energy is quantized into energy levels.

o If electron energy is not quantized, then a continuous spectrum would be observed.

o The energy of the energy levels is governed by: , where E is energy and n is the energylevel.

The equation is negative, so all energies are negative. Negative energies mean that it is energy that contributes to the "stability" of the system - the

electron binding energy. The more negative (lower) the energy, the more stable the orbit, the harder it is to knock out

the electron. The less negative (higher) the energy, the less stable the orbit, the easier it is to knock out the

electron. At the highest energy, 0 eV, there is no binding energy, so the electron dissociates. For atoms other than hydrogen, the shape of the energy level curve stays the same. However,

the numerator is a constant other than 13.6 eV.

The precise relationship for atoms other than hydrogen is: , where Z is the atomicnumber.

Higher Z values give more negative binding energy (more stable) because the more charge, themore electrostatic attraction.

calculation of energy emitted or absorbed when an electron changes energy levelso The wavelength of the emitted or absorbed radiation is governed by the Rydberg formula:

, where lambda is the wavelength, nf is the final energy level, ni is the initial energylevel, and R is the rydberg constant.

o The energy of the emitted or absorbed radiation is: , where E is energy, f and vboth mean frequency and c is the speed of light.

o Energy is emitted for transitions to lower energy levels (nf < ni).o Energy is absorbed for transitions to higher energy levels (nf > ni).

Atomic Nucleus

Atomic number, atomic weight

Atomic number = the number of protons.o The atomic number is what defines an element.o When two things have the same number of protons, they are the same element.

Atomic weight = the weighted average of atomic mass for all isotopes of a given atom.o Atomic mass = number of protons + neutrons.o The atomic mass is used for an isotope.o The atomic weight is used for an element.

In standard notation the atomic number is always at the bottom, and the weight is always on top:

An easy way to remember this is that the atomic number is "fundamental" to the identity of the element, so it islocated at the fundation.

Neutrons, protons, isotopes

Neutrons = neutral particles that reside in the nucleus. Protons = positive particles that reside in the nucleus. Isotopes = things with the same number of protons, but different number of neutrons.

Atomic particles

Name Mass (amu) Charge Location

Proton 1 +1 In the nucleus

Neutron 1 0 In the nucleus

Electron 0 -1 Surrounding the nucleus

Nucleons = protons or neutrons.

Isotopes

When two things have the same number of protons but different number of neutrons, they are isotopes of thesame element.

Isotopes often have similar chemical properties, but different stabilities (some decay and give off radiation,some don't).

Nuclear forces

Two forces are at work in the nucleus: the strong force and the electromagnetic force. The strong force binds the nucleons together, and is therefore contributes to the binding energy. The electromagnetic force is due to electrostatic repulsion between the positively charged protons in the

nucleus. The nucleus stays together because the strong force is much stronger than the electromagnetic repulsion. The strong force is also called the "nuclear force".

... see forces section

Radioactive decay: alpha, beta, gamma, half-life, exponential decay, semi-log plots

Alpha decay: . Ejection of a helium nucleus at relatively low speed.

Beta decay: . Ejection of a high speed electron.

Gamma decay: . Release of high energy electromagnetic wave.

Name Notation Information

Alphaparticle

Weakest form of radiation. Can be stopped by a sheet of paper. It is essentially a relativelylow speed helium nucleus.

Betaparticle

More energy than an alpha particle. Can be stopped by aluminum foil. It is a high speedelectron.

Gamma rayStrongest form of radiation. It is a high energy electromagnetic wave. Can be stopped by athick layer of lead or concrete.

Some notes on α, β, and γ decayo Conservation of mass dictates that total atomic weight before the decay equal the total atomic weight

after.o Conservation of charge dictates that the total atomic number before the decay equal the total atomic

number after.o Don't get thrown off by particles you do not recognize. As long as they have a weight and a charge, just

incorporate these numbers in your calculations.o MCAT problems on identifying decay products are just math work.o Remember: the atomic number (the bottom number) determines what element it is.

half-life is the time it takes for the amount of something to half due to decay.o After 1 half-life, the amount of the original stuff decreases by half.o After 2 half-lives, the amount of the original stuff decreases by a factor of 4.o After 3 half-lives, the amount of the original stuff decreases by a factor of 8.

o The mathematical expression for this is: , where N sub t=0is the amount the original starting material. N sub t is the amount of the original material that is still left.Lastly, t is time.

o Although the above is the official half-life equation, people like to multiply rather than to divide.

Therefore, a more user friendly equation is: Stability

o When something is stable, it doesn't decay.o When something is unstable, it decays.o The more unstable something is, the shorter the half-life.

Exponential decay:

Semi-log plots: for the purposes of the MCAT, semi-log plots convert exponential curves into straight lines.o Something that curves up becomes a straight line with a positive slope.o Something that curves down becomes a straight line with a negative slope.

o For exponential decay, a semi-log plot graphs the log of amount vs. time.o For exponential decay, a semi-log plot is a straight line with a negative slope.o The semi-log plot intercepts the x axis where the original y value is 1.

o

General nature of fission

Fission = one nuclei splitting apart. Uranium undergoes fission when struck by a free neutron. The fission of uranium generates more neutrons, which goes on to split other Uranium nuclei. This is called a

chain reaction.

General nature of fusion

Fusion = two nuclei coming together. The Sun works by fusion. Hydrogen in the Sun fuses to form helium.

Mass deficit, energy liberated, binding energy

Mnucleons = Matom + binding energy/c2

Mnucleons > Matom because some of the Mnucleons is converted to binding energy that holds the nucleons together.o Mnucleons = mass of all the nucleons that make up the atom in their free, unbound state.o Matom = mass of the atom.o Mnucleons - Matom = mass deficit (also called mass defect) = ΔM.o Binding energy = converting ΔM into its equivalent in energy = ΔM c2.o Energy liberated = binding energy.

The conservation of mass and energy: the total mass and energy before a reaction is always the same as thetotal mass and energy after the reaction.

If the total mass before the reaction is different from the total mass after the reaction, then the difference inmass is made up for by energy.

The difference in mass before and after a reaction is called the mass deficit or mass defect.

The energy that makes up for the mass deficit is calculated by: Energy is liberated when mass is lost during a reaction. Energy is absorbed with mass is gained during a reaction. More notes on binding energy:

o Binding energy most commonly refers to nuclear binding energy (the energy that binds the nucleonstogether).

o Binding energy is due to the strong force. ...more on forceso Binding energy per nucleon is strongest for Iron (Fe 56).o Binding energy per nucleon is the weakest for Deuterium (the 2-nucleon isotope of hydrogen).o Less commonly used is the electron binding energy. This is because electron binding energy is more

commonly referred to as the ionization energy.