Pre-AP Physics – Chapter 1 Notes – Yockers – JHS 2008

Standards of Length, Mass, and Time ( quantities)- length –

- mass –

- time –

Derived Quantities: Examples –

Dimensional Analysis – useful to check equations and to assist in deriving expressions- L = length; M = mass; and T = time

Conversion of Units – multiplying a quantity by a conversion factor ( ) withnumerator and denominator having different units to provide the desired units in the final result. Importance?!

Geometry / Trigonometry / Algebra

Significant Figures – measured values are known only to within the limits of experimentaluncertainty (quality of apparatus, skill of experimenter, number of measurements)- When ,the number of significant figures in the final answer is the

same as the number of significant figures in the quantity having the number ofsignificant figures.

- When numbers are , the number of decimal places in the result shouldequal the smallest number of decimal places of any term in the sum.

- After you are done with Chapter 1 (and for the AP Exam) significant figures is a goodguideline.

Coordinate Systems – used to specify locations in space consist of- a fixed reference point O, called the - a set of specified axes or directions with - instructions that explain how to label a point in space relative to the origin and axes- the (rectangular) and/or coordinate systems will be used unless

specified

Vectors and Scalars- scalar – a quantity that is completely specified by a positive or negative number with

appropriate - vector – a quantity that must be specified by both

→since velocity, v, is a vector, it should be written as either v or →velocity’s magnitude (always positive) could be written as v or

Pre-AP Physics – Chapter 2 Notes – Yockers – JHS 2008KINEMATICS (1-Dimensional Motion)

Motion/Strobe diagrams

Importance of coordinate systems and specifying direction of vectors

Displacement –

(general) where ∆d = displacement (change in position)

- displacement for an object at rest = - displacement can be positive or negative- displacement does not equal

(horizontal) (vertical)

- displacement has both magnitude and direction (vector)→vector is a physical quantity that requires the specification of both

→scalar is a quantity that has

Velocity – the quantity that measures how

Average velocity – total displacement divided by the time interval during which the displacementoccurred (m/s)

- speed does not equal →velocity has magnitude and direction, and speed only has

- average velocity can equal slope if ∆s and ∆t are graphed→steeper slope = →position-time graph that is parallel to time axis (x axis) has a position that does not

change over time (velocity of m/s)- slope allows you to determine vavg over short or long time intervals

→instantaneous velocity – the limit of the average velocity as the time interval ∆tbecomes infinitesimally short

→the slope of the line tangent to the position-time curve at a given point is theinstantaneous velocity at that corresponding time

→instantaneous speed (scalar) – is defined as the magnitude of the instantaneousvelocity (speed can never be negative)

- equation of motion for average velocity

Pre-AP Physics – Chapter 3 Notes – Yockers – JHS 2008KINEMATICS (1-Dimensional Motion)

Acceleration – - velocity-time graphs- motion/strobe diagrams

Average acceleration – the change in velocity divided by the time interval during which the changeoccurs

(m/s)/s = m/s2

- acceleration is a vector quantity (direction and magnitude)- acceleration can be either

→when an object’s velocity and acceleration are in the direction, the speed of theobject with time

→when an object’s velocity and acceleration are in directions, the speed of theobject with time

One-dimensional motion with constant acceleration- when acceleration is constant, average acceleration equals instantaneous acceleration

or

- for constant acceleration (final velocity with average acceleration)

- since velocity is increasing or decreasing uniformly with time (constant a), the averagevelocity in any time interval can be expressed as the arithmetic average of the initialvelocity and the final velocity

- now we can determine the displacement of an object as a function of time

( ) ffiiffi

ifavgif tvvdtvv

dtvdd

++=

++=+=

21

2 or, by substituting favgif tavv +=

remember, this is for a constant a

- to relate displacement, velocity, and acceleration without time

(di is usually considered to be 0)

Free-fall- a freely falling object is an object moving under the influence of only, regardless of its

initial motion- objects “thrown” upward or downward and those released from rest are all falling freely once

they are - once in free-fall, all objects have an acceleration , which is the free-fall acceleration

g ( m/s2)- all of the previous formulas can be applied to free-fall situations by replacing the general

displacement symbol s with the vertical displacement symbol y

Pre-AP Physics – Chapter 4 Notes – Yockers – JHS 2008Forces In One Dimension (Newton’s Laws)

Force – represents the interaction of an object with its - forces cause - SI unit for force is the newton (N)

→1 N equals the amount of force that, when acting on a 1 kg mass, produces anacceleration of 1 m/s2

→1 N = 1 kg x 1 m/s2

→F = ma- forces can act through

→contact forces – →field forces – exists between objects

- gravity (gravitational field)- electricity (electric field)- magnetism (magnetic field)

→fundamental forces that act on elementary particles are all field forces- force depends upon (force is a quantity)- diagrams that show force vectors as arrows are called - free-body diagrams are used to analyze only the forces affecting the motion of

Newton’s First Law- what is the motion of an object before forces are applied?

→will an object with no force acting on it always be at rest?- Galileo realized (1630s) that a block sliding on a perfectly smooth surface would

in the absence of an →an object’s nature is to maintain its →Newton developed this idea further

- Newton’s first law (the Law of Inertia) – when the net external force on an object is , itsacceleration is →inertia – the tendency of an object →net external force can be determined by a

- an object’s change in motion is the same as if the were theonly force acting on the object

→external force is a single force that acts on an object as a result of the interactionbetween the object and its environment

→net external force is the - mass is a measurement of in a body

→which has more inertia?- bowling ball or a golf ball?- football: lineman or runningback?

→inertia is directly proportional to - ↑mass→↓body accelerates under an applied force

- equilibrium – the state of a body in which there is →→

- Newton’s first law describes equilibrium –

→a body is in equilibrium when

Newton’s Second Law – force is proportional to - the acceleration of an object is directly proportional to the net external force acting on the

object and inversely proportional to the mass of the object↑F→↑a (constant m)↓m→↑a (constant F)

or

→if the net external force is zero, then- - -

Newton’s Third Law – force always exists in pairs (action-reaction pair);

- if two bodies interact, the magnitude of the force exerted on object 1 by object 2 isequal to the magnitude of the force simultaneously exerted on object 2 by object 1, and the two forces are opposite in direction

- for every action there is an →action-reaction pair→remember, reaction force occurs at as the action force→thus, either force can be considered either the action force or the reaction force

- action-reaction pairs may not result in equilibrium because they act

Weight – measure of the magnitude of exerted on an object- 1 lb = 4.448 N- 1 N = 0.225 lb- Fg (W) is the force exerted by the Earth on an object ( )

→because weight is dependent on gravity, weight depends on →remember, does not change→weight is not an inherent property of an object→objects weigh less at higher altitudes because ag decreases with increasing distance

from the center of the Earth

Normal Force (FN)- normal also means - normal force is a contact force exerted by one object on another in a direction perpendicular

to the

Pre-AP Physics – Chapter 5 Notes – Yockers – JHS 2008Forces in Two Dimensions

Force of Friction- Fs is the force of - Fs,max occurs when the applied is as great as it can be without causing an object to

(the force of static friction reaches its maximum value)- Fk is the force of kinetic friction which will be less than Fs,max because

(cold-welding; intermolecular forces between an object and a surface) cannot form

- force of friction also depends on the of the surfaces in contact- coefficient of friction (µ) – of the force of friction to the normal force acting

between two objects

-coefficient of friction is a ratio of forces ( )→µk will always be lower than µs

→a value of 1.0 for µs indicates

Air Resistance (FR) – acts in the direction to an object’s motion- magnitude of FR, FR, is usually proportional to the

vFR ∝

- when FR = F in the opposite direction, a = 0 m/s2

- in freefall, when FR = Fg, a = 0 m/s2, ( ) has been reached

Pre-AP Physics – Chapter 6 Notes – Yockers – JHS 2008MOTION IN TWO DIMENSIONS

Free-fall- a freely falling object is an object moving under the influence of only, regardless of its

- objects “thrown” upward or downward and those released from rest are all falling freely oncethey are

- once in free-fall, all objects have , which is the free-fall accelerationg ( )

- all of the kinematic formulas can be applied to free-fall situations by replacing the generaldisplacement symbol d with the vertical displacement symbol y

Projectile Motion (2-Dimensional)- assumptions

→the free-fall acceleration, ag or g, has a magnitude of 9.8 m/s2, isover the range of motion, and is directed

(so ag or g = -9.8 m/s2)→the effect of air resistance is →the rotation of the Earth

- motion in the x direction (constant – no )

- motion in the y direction

- speed of the projectile and its direction at any instant can be calculatedfrom the components of the velocity at that instant

Circular Motion- for an object moving in a circular path with a , acceleration is due to a change

in - centripetal acceleration

→remember 0

0

ttvv

af

f

−−

=

and that velocity can be changed either by or

; a change in either produces →centripetal acceleration (ac) – acceleration directed toward the

- magnitude of ac is given by

Causes of Circular Motion- forces maintain circular motion

→an object in a circular path is accelerating because the direction (not magnitude) of itsvelocity is

→the acceleration is →the of an object would “prefer” a straight-line path but centripetal acceleration

maintains a →the magnitude of the force causing the centripetal acceleration can be calculated by

- a force directed toward the is necessary for circular motion→force acting to motion will change velocity→if this force vanishes, motion begins tangent to the circular path

- free-fall?- projectile motion?

- inertia is often misinterpreted as a →mobile phone on dash board

- is friction enough to hold it in place?- side of care will provide enough force to put the mobile phone into the circular

path the car is following

Relative Velocity Problems – there is no “set” way of attacking these problems, so be sure youpractice!

Pre-AP Physics – Chapter 7 & 8 Notes – Yockers – JHS 2008The Law of Gravity and Rotational Motion

Newton’s Universal Law of Gravitation- planets move in nearly circular orbits around the Sun- gravitational force causes these nearly circular orbits- gravitational force is the natural force of attraction between any two objects in the

universe (a field force)→→→not just large objects (stars, planets, etc.)

→gravitational force acts in →the of the fundamental forces→the gravitational force is always →Newton’s law of universal gravitation – every particle in the Universe attracts every

other particle with a force that is directly proportional to the product of themasses of the particles and inversely proportional to the square of the distancebetween them

- G = 6.67 x 10-11 N·m2/kg2 (the universal gravitational constant)- r is the distance between the of the two particles

→the gravitational field at the surface of a planet

- if r is equal to the radius of the planet, this equation gives the acceleration dueto gravity at the of the planet

Rotational quantities- rotational motion – motion of a body that - axis of rotation – - circular motion – occurs when any single point on an object travels in a circle around an axis

of rotation→r – radius→s – arc length –

- angles can be measured in radians→radian – an angle whose arc length is equal to its radius

→rad = radian(s); 1 rad = arc length/length of radius when s=r; °≈°= 3.572

3601π

rad

→ the radian is →in general, any angle, θ, measured in radians, is defined by the relation

→conversions

- angular displacement, ∆θ, describes how much an object has →the angle through which a point, line, or body is rotated in a specified direction and

about a specified axis→ ∆θ - angular displacement

- ∆s is positive (+) when rotation is - ∆s is negative (-) when rotation is

- angular speed, ω, describes →the rate at which a body rotates about an axis, usually expressed in →average angular speed = ωavg

unit is rad/s or revolutions/unit time

- angular acceleration, α, occurs when →the time rate of change of angular speed, expressed in rad/s/s or rad/s2

→average angular acceleration = αavg

- all points on a rotating rigid object have the same angular acceleration and angular speed→if not,

- similarities of angular and linear quantitieslinear

angular

x θv ωa α

Comparing angular and linear quantities- linear kinematics

)(221

20

2

200

0

davv

attvdd

tavv

f

f

f

∆+=

++=

∆+=

- angular kinematics

Tangential and centripetal acceleration- objects in circular motion have a - an object farther from the axis of rotation must travel at a tangential speed around the

circular path, ∆s, to travel the same as would an object closer to

the axis- tangential speed

ω must be measured in rad/s

- tangential acceleration is tangent to the →the instantaneous linear acceleration of an object directed along the tangent to the

object’s circular path

→α must be measured in rad/s2

- centripetal acceleration

→remember 0

0

ttvv

af

f

−−

=

and that velocity can be changed either by or

; a change in either produces →for an object moving in a circular path with a constant speed, acceleration is due to a

change in →centripetal acceleration (ac) – acceleration directed toward the of a circular

path- magnitude of ac is given by

- because tangential speed is related to the angular speed by ωrvt = , thecentripetal acceleration can also be found using angular speed

- tangential and centripetal accelerations are →tangential component of acceleration is due to changing →centripetal component of acceleration is due to changing

- total acceleration is found using the Pythagorean theorem

- direction of the acceleration can be found using

Causes of Circular Motion- forces maintain circular motion

→an object in a circular path is accelerating because the direction (not magnitude) of itsvelocity is constantly changing

→the acceleration is centripetal or directed toward the center of motion

→the inertia of an object would “prefer” a path but centripetal accelerationmaintains a path

→the magnitude of the force causing the centripetal acceleration can be calculated by

- a force directed toward the is necessary for circular motion→force acting ┴ to motion will change →if this force vanishes, straight-line motion begins tangent to the circular path

- free-fall?- projectile motion?

- inertia is often misinterpreted as a force→mobile phone on dash board

- is friction enough to hold it in place?- side of care will provide enough force to put the mobile phone into the circular

path the car is following

Torque - τ (tau) – SI derived unit is N·m- point mass vs. extended object

→extended object – has a →point mass – assuming all of an object’s mass is

- rotational and translational motion can be separated→translational motion – →rotational motion –

- net torque produces rotation→torque – a quantity that measures the ability of a force to an object

about some axis- torque depends on

→how easily an object rotates depends not only on how much force is applied but alsoon the force is applied

→lever arm – the ┴ distance from the axis of rotation to a line drawn along the directionof the force

- torque also depends on the →forces do not have to be to cause rotation

- two equal but opposite forces can produce a rotational acceleration if they do not act alongthe same line

- if torques are equal and opposite, there will be no rotational acceleration→seesaw – momentary torque produced by pushing with legs

Rotational Equilibrium- equilibrium requires

→if the net force on an object is zero, the object is in equilibrium→if the net torque on an object is zero, the object is in equilibrium

- the dependence of equilibrium on the absence of net torque is called the second condition ofequilibrium→the resultant torque acting on an object in rotational equilibrium is independent of

where the axis is placed- an unknown force that acts along a line passing through this axis of rotation will

- beginning a diagram by arbitrarily setting an axis where a force acts caneliminate an unknown in a problem

- conditions for equilibriumType of Equation Symbolic Eq. Meaning

translational ΣFnet=0 Fnet on an object must be zerorotational Στnet=0 τnet on an object must be zero

- unstable equilibrium – - stable equilibrium –

Pre-AP Physics – Chapter 9 Notes – Yockers – JHS 2008Momentum & Impulse

Momentum – describes an object’s - a vector quantity defined as the product of an object’s

→p is momentum→direction matches that of →derived unit =

- a change in momentum takes →momentum is closely related to

Impulse – for a constant external force, the product of the force and the time over which it acts on anobject- impulse-momentum theorem

→F∆t = =→impulse is a

- all forces exerted on an object are assumed unless otherwise noted- stopping times and stopping distances depend on the impulse momentum theorem- a change in momentum over a longer time requires less force

Conservation of Momentum- momentum is always - law of conservation of momentum – the total momentum of all objects interacting with one

another remains constant regardless of the nature of the forces between the objects→momentum is conserved in →momentum is conserved for objects

- Newton’s third law leads to conservation of momentum→for the forces in a collision involving two objects

→momentum and the collision

- forces involved in a collision are treated as though they are →in a real collision things are a bit more complicated!→we work with average forces

Elastic and Inelastic collisions- two extreme types of collisions

→→

- perfectly inelastic collision – a collision in which two objects and move with a after colliding

→objects become essentially →final mass is equal to the →move with the

→remember, signs for direction are important!→K does not remain constant in inelastic collisions

- some K is converted to heat, sound, internal K, and internal U (deformation,etc.)

- elastic collision – a collision in which the →objects maintain their original shapes and are not by the action of forces

- most collisions are neither elastic nor perfectly inelastic→→

- most collisions fall into a category between the two extremes→inelastic collisions – colliding objects bounce and move separately after the collision,

but K decreases in the collision- K and p are both conserved in

→remember, signs (+/-) are important- glancing collisions

→colliding masses rebound at some relative to the line of motion of the incidentmass

→momentum is conserved in all collisions when no external forces are acting

→total momentum is conserved along the and

Pre-AP Physics – Chapter 10 Notes – Yockers – JHS 2008Work & Energy

Work – a force that causes a displacement of an object does - using d instead of ∆s

→work equals the magnitude of the force, F, times the magnitude ofthe

→work is not done unless an object is due to the action of aforce

→the of a force alone does not constitute work- work is done only when components of a force are to a displacement

→the component to the direction of an object’s displacement does work→components to a displacement do no work

- derived unit for work is the joule (J) or N·m (after James Prescott Joule 1818-1889)- the sign of work is important

→work is scalar and can be “+” or “-“- work is positive when the component of force is in the as the

displacement- work is negative when the force is in the direction the displacement- cosθ is negative for angles greater than 90° but less than 270°- cosθ is positive for angles less than 90° but greater than 270°

→perpendicular to direction of displacement – - cos(90°) = - cos(270°) =

- if the work done on an object results only in a change in the object’s speed, the sign of thenet work indicates whether speed is increasing or decreasing→”+” work → ↑ in speed and force ect→”-“ work → ↓ in speed and

Energy - kinetic energy (K) – associated with an object in

→K is a scalar quantity dependent upon

→SI unit is the joule (J) or N·m

Work, Energy, and Power- work-kinetic energy theorem

→relates the work done on an object to the change in kinetic energy

→work is a method of transferring - power

→→

and since W = Fd

→SI unit for power is the watt (W) (James Watt 1736-1819)- 1 W = 1 J/s- 1 horsepower = 746 W

→machines with different power ratings do the same work in

Simple Machines- machine – any device that transmits or modifies force, usually by changing the force applied

to an object- all machines are combinations of six fundamental types of machines (simple machines)

→- mechanical advantage – comparison of how large the

is relative to

- claw hammer example

- machines can alter the force and the distance moved, but the work done on the object(product of F x d) is

- mechanical advantage of an ideal machine

→in a real system, some of the work done by the force is - efficiency is a measure of how well a machine works

→efficiency is a measure of how much input energy is lost (friction) compared with howmuch energy is used to perform

→efficiency of an ideal machine is →efficiency also equal to the mechanical advantage divided by the ideal mechanical

advantage

Pre-AP Physics – Chapter 11 Notes – Yockers – JHS 2008Energy and Its Conservation

Energy - kinetic energy (K) – associated with

→K is a scalar quantity dependent upon

→SI unit is the joule (J) or N·m- potential energy (U) – stored energy – energy associated with an object due to

→describes an object that has the potential to move because of →depends not only on the properties of an object but also on the object’s

→U is a scalar quantity→SI unit is the joule (J) or N·m

- gravitational potential energy (Ug) – depends on →potential energy associated with an object due to its position relative to the Earth of

some other gravitational source

→note that ag and h are of an object→ Ug is a result of an object’s position, so it must be measured relative to some

where Ug = - elastic potential energy (Us) – depends on distance

→the potential energy in a stretched or compressed elastic object- elastic – capable of recovering

→relaxed length – the length of a spring when no external forces are acting on it

- k is the spring constant or force constant →a parameter that expresses how a spring (or elastic material) is

to being →SI unit is N/m

- x is the distance compressed or stretched- mechanical energy (ME) – the sum of and all forms of

associated with an object or group of objects→is not a unique form of energy like the energies listed above→is not necessarily related to →all energy that is not mechanical energy is classified as energy

-

Conservation of Energy- conserved quantity – remains constant but may change - conservation of mechanical energy

→in the absence of friction, mechanical energy remains the same→mathematical expression depends on the forms of energy in a given situation→conservation of energy occurs even when acceleration varies as long as

- mechanical energy is not conserved in the presence of →total energy is always conserved→heat energy is not mechanical, so energy is “lost” from the mechanical energy system

KE in Elastic and Inelastic Collisions- momentum is always - law of conservation of momentum – the total momentum of all objects interacting with one

another remains constant regardless of the nature of the forces between the objects→momentum is conserved in →momentum is conserved for objects

- perfectly inelastic collision – a collision in which two objects stick together and move with acommon velocity after colliding→K does not remain constant in

- some K is converted to heat, sound, internal K, and internal U (deformation,etc.)

- elastic collision – a collision in which the total momentum and the total K remain constant→K and p are both conserved in

Pre-AP Physics – Chapter 12 Notes – Yockers – JHS 2008Thermal Energy

Defining Temperature- adding or removing energy changes - temperature is proportional to the of atoms/molecules

→monatomic gases → →other substances → molecules can rotate and/or vibrate

- - -

- temperature is meaningful only when it is (zeroth law of thermodynamics)→thermal equilibrium – the state in which two bodies in physical contact with each

other have - basis for measuring temperature with thermometers- the temperature of any two objects at thermal equilibrium always

- matter expands as its temperature →thermal expansion – as the temperature of a substance increases, so does its

- thermal expansion characteristics of a material are indicated by a quantitycalled the

- between 0°C and 4°C the volume of water- measuring temperature

→calibrating thermometers requires - ice point (0°C) mixture of water and ice at 1 atm- steam point (100°C) mixture of steam and water at 1 atm- degrees are

→Fahrenheit (US)→Celsius (centigrade) – SI

→the possible problem with the above temperature scales is that they can have

→because kinetic energy, K, of atoms/molecules in a substance always has a positivevalue, the temperature that is a measure of that energy should also have positivemagnitudes- Kelvin scale

→absolute zero – →→ 0 K =

Heat and Energy- heat (Q) – energy transferred between objects of

→heat (energy) moves from a temperature to a temperature- heat has units of joules

→work, K, and U→1 calorie = 4.186 J (Cal = kcal)

- conservation of energy

→

Changes in Temperature and Phase- there is a property of all substances that causes their temperatures to vary by different

amounts when equal amounts of energy are added to or removed from them→result of the ease with which atoms and molecules within a substance

- how easily the temperature of a substance can change→specific heat capacity (specific heat)

- relates

- cp = - Q = - m = - ∆T =

→specific heat capacity can be used for both- -

→when ∆T and Q are positive (+), energy is transferred the substance→when ∆T and Q are negative (-), energy is transferred the substance

Calorimetry- uses the well know specific heat of water (4186 J/kg·°C) and a calorimeter to determine

specific heat capacity of different substances using the following relationships

or

→w = water→x = substance

Latent Heat and Phase Change- all phase changes involve a change in

→no change in temperature ( )→there is a change in matter ( )

- the energy required to change the phase of a given mass m of a puresubstance is where L is the latent heat of the substance

→latent heat – →L depends upon the →L depends upon the →the proper sign is chosen according to the direction of the energy flow

- ice to water – - water to ice –

- latent heats→Lf – latent heat of fusion – when phase change involves

→Lv – latent heat of vaporization – when phase change involves

→latent heats vary considerably between substances and Lf and Lv

-the latent heat of vaporization for a given substance is usually larger than thelatent heat of fusion

- in the change from solid to liquid phase, solid bonds between molecules aretransformed into somewhat weaker liquid bonds

- in the change from liquid to gas phase, however, liquid bonds are broken,creating a situation in which the molecules of the gas have essentially nobonding to one another

- more energy is therefore required to vaporize a given mass of a substance thanto melt it

- with a knowledge of latent heat, it is possible to understand the full behavior of a substanceas energy is added to it

The First Law of Thermodynamics- energy conservation requires that the total change in internal energy from its initial to its final

equilibrium conditions be equal to the transfer of energy by both heat and work

→remember that 0UUU f −=∆→change must be equal to the transfer of energy by both

- the change in internal energy of a system is zero in a →cyclic process – a thermodynamic process in which a system returns to the same

conditions under which it started- heat engines use heat to do work

The Second Law of Thermodynamics- no machine can be made that only absorbs energy by heat and then entirely transfers the

energy out of the engine by an equal amount of work- thermodynamic efficiency

→Qh = →Qc =

Heat and EntropyNote – will entropy (S) increase, decrease, or remain the same during a particular process- entropy ≡ a measure of the

→entropy can be regarded as an index of

→the 2nd Law of Thermodynamics is really a statement of

- the more disordered a system is, - the entropy of the Universe increases in all natural processes (another way of stating the 2nd

Law of Thermodynamics)→there are processes in which the entropy of a system (A) decreases, but this must be

accompanied by a net increase in entropy of some other system (B)→the change in entropy of system B is greater than the change in entropy of system A