Linear MotionLinear motion is the motion in 1 dimension (1-D) or the motion in a straight line.

Distance1) The distance traveled by an object is the total length that is traveled by that object.2) Distance is a scalar quantity.3) The SI unit of distance is m (metre).Displacement

1) Displacement of an object from a point of reference, O is the shortest distance of the object from point O in a specific direction.2) Displacement is a vector quantity.3) The SI unit of displacement is m (metre).

Distance vs Displacement

Distance travelled = 200mDisplacement = 120 m, in the direction of NortheastSpeed1. Speed is the rate of change in distance. It is a measure of how fast the distance change in a movement.2. Speed is a scalar quantity.3. The SI unit of speed is m/s (metre per second)

Equation of Speed

Velocity1. Velocity is define as the rate of displacement change. It is the measure of how fast the displacement change of a moving object.2. Velocity is a vector quantity.3. The unit of displacemnet is m/s (metre per second)

Equation of velocity

Positive or Negative Sign of Velocity1. In velocity, the positive/negative sign indicates direction.2. You can take any direction as positive and the opposite as negative.3. For a linear motion, normally we take the motion to the right as positive and hence the motion to the left as negative.Acceleration

Acceleration is the rate of velocity change.Acceleration is a vector quantity. It is a measure of how fast the velocity change.Acceleration is a vector quantity.The unit of acceleration is ms-2.

EquationAdditional NotesAn object moves with a constant velocity if the magnitude and direction of the motion is always constant.An object experiences changes in velocity if the magnitude of velocity changes the direction of the motion changes.An object that experiences changes in velocity is said to have acceleration.An object traveling with a constant acceleration, a, if the velocity changes at a constant rate.

Equation of Uniform AccelerationMost of the motion problems can be solved by the following equations. Therefore, make sure that you memorise all of them.

How we know when to use the equation?

There are 3 types of motion: motion with uniform velocity motion with uniform acceleration motion with changing accelerationThe 4 equations are used when the motion is uniform acceleration.Motion with changing acceleration is not in SPM Physics syllabus. It will be discussed in Form 5 add maths.

Ticker Timer

A ticker-timer consists of an electrical vibrator which vibrates 50 times per second. This enables it to make 50 dots per second on a ticker-tape being pulled through it. The time interval between two adjacent dots on the ticker-tape is called one tick. One tick is equal to 1/50 s or 0.02 s.

Uniform Velocity The distance of the dots is equally distributed. All lengths of tape in the chart are of equal length. The object is moving at a uniform velocity.

Uniform Acceleration The distance between the dots increases uniformly. The length of the strips of tape in the chart increase uniformly. The velocity of the object is increasing uniformly, i.e. the object is moving at a constant acceleration.

Uniform Deceleration The distance between the dots decreases uniformly. The length of the strips of tape in the chart decreases uniformly. The velocity of the object is decreasing uniformly, i.e. the object is decelerating uniformly.Finding VelocityVelocity of a motion can be determined by using ticker tape through the following equation:

Caution!:t is time taken from the first dot to the last dot of the distance measured.

Displacement - Time Graph

In a Displacement-Time Graph, the gradient of the graph is equal to the velocity of motion.

Analysing Displacement - Time GraphGradient = 0Hence, velocity = 0

Gradient is constant,hence, velocity is Uniform

Gradient is negative and constant, hence velocity is uniform and in opposite direction

Gradient is increasing, hence velocity is increasing.

Gradient is decreasing, hence velocity is decreasing.

Velocity - Time Graph

The gradient of the velocity-time gradient gives a value of the changing rate in velocity, which is the acceleration of the object. The area below the velocity-time graph gives a value of the object's displacement.

Analysing Velocity-Time GraphUniform velocity

Uniform acceleration

Increasing acceleration

Uniform deceleration

Decreasing acceleration

Converting a Velocity-Time graph to Acceleration-Time graph

In order to convert a velocity-time graph to acceleration time graph, we need to find the gradient of the velocity time graph and plot it in the acceleration-time graph.Free falling is a motion under gravitational force as the only force acting on the moving object. In SPM, you need to know the graphs of free falling of the following movement1. Launching object upward.2. Dropping Object from High Place3. Object Falling and Bounce BackLaunching Object Upward

Velocity-Time GraphAcceleration-Time Graph

Dropping Object from High Place

Velocity-Time GraphAcceleration-Time Graph

Object Falling and Bounce Back

Velocity-Time GraphAcceleration-Time Graph

MassMass is defined as the amount of matter. The SI unit of mass is kilogram (kg)Mass is a scalar quantity.

InertiaInertia is the property of a body that tends to maintain its state of motion.

Newton's First LawIn the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).

Jerking a Card

When the cardboard is jerked quickly, the coin will fall into the glass.

Explanation: The inertia of the coin resists the change of its initial state, which is stationary. As a result, the coin does not move with the cardboard and falls into the glass because of gravity. Pulling a Book

When the book is pulled out, the books on top will fall downwards.

Explanation: Inertia tries to oppose the change to the stationary situation, that is, when the book is pulled out, the books on top do not follow suit.Pulling a Thread

1. Pull slowly - Thread A will snap.

Explanation: Tension of thread A is higher than string B. Tension at A = Weight of the load + Pulling Force 2. Yank quickly - Thread B will snap.

Explanation: The inertia of the load prevents the force from being transmitted to thread A, hence causing thread B to snap. Larger Mass - Greater Inertia

Bucket filled with sand is more difficult to be moved. It's also more difficult to be stopped from swinging.

Explanation: Object with more mass offers a greater resistance to change from its state of motion. Object with larger mass has larger inertia to resist the attempt to change the state of motion.Empty cart is easier to be moved

An empty cart is easier to be moved compare with a cart full with load. This is because a cart with larger mass has larger inertia to resist the attempt to change the state of motion.

MomentumMomentum is defined as the product of mass and velocity.Momentum is a vector quantity. It has both magnitude and direction.The SI unit of momentum is kgms-1

Formula:

Principle of Conservation of MomentumThe principle of conservation of momentum states that in a system make out of objects that react (collide or explode), the total momentum is constant if no external force is acted upon the system.Sum of Momentum Before Reaction= Sum of Momentum After Reaction

Formula

ExplosionBefore explosion both object stick together and at rest. After collision, both object move at opposite direction.

Total Momentum before collision Is zeroTotal Momentum after collision :

m1v1 + m2v2

From the law of conservation of momentum:Total Momentum Before collision = Total Momentum after collision

0 = m1v1 + m2v2

m1v1 = - m2v2

(-ve sign means opposite direction)

Examples or Application of Conservation of Momentum in Explosion1. Fire a pistol or rifle2. Launching a rocket3. Application in jet engine4. Fan boatElastic CollisionElastic collision is the collision where the kinetic energy is conserved after the collision.Total Kinetic Energy before Collision= Total Kinetic Energy after CollisionAdditional notes: In an elastic collision, the 2 objects separated right after the collision, and the momentum is conserved after the collision. Total energy is conserved after the collision.

Inelastic CollisionInelastic collision is the collision where the kinetic energy is not conserved after the collision.Additional notes: In a perfectly elastic collision, the 2 objects attach together after the collision, and the momentum is also conserved after the collision. Total energy is conserved after the collision.Rocket1. 1Mixture of hydrogen and oxygen fuels burn in the combustion chamber.2. Hot gases are expelled through the exhausts at very high speed .3. The high-speed hot gas produce a high momentum backwards.4. By conservation of momentum, an equal and opposite momentum is produced and acted on the rocket, pushing the rocket upwards.Jet Engine1. Air is taken in from the front and is compressed by the compressor.2. Fuel is injected and burnt with the compressed air in the combustion chamber.3. The hot gas is forced through the engine to turn the turbine blade, which turns the compressor.4. High-speed hot gases are ejected from the back with high momentum.5. This produces an equal and opposite momentum to push the jet plane forward.Force1. A force is push or pull exerted on an object.2. Force is a vector quantity that has magnitude and direction.3. The unit of force is Newton ( or kgms-2).Unbalanced Force/ Resultant Force When the forces acting on an object are not balanced, there must be a net force acting on it. The net force is known as the unbalanced force or the resultant force.When a force acts on an object, the effect can change the1. size,2. shape,3. stationary state,4. speed and5. direction of the object.Newton's Second LawThe rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction.Implication:When there is resultant force acting on an object, the object will accelerate (moving faster, moving slower or change direction).

Formula of Force

From Newton's Second Law, we can derived the equation(IMPORTANT: F Must be the net force)

Summary of Newton's 1st Law and 2nd Law

Newton's First Law:When there is no net force acting on an object, the object is either stationary or move with constant speed in a straight line.

Newton's Second Law:When there is a net force acting on an object, the object will accelerate.ImpulseImpulse is defined as the product of the force (F) acting on an object and the time of action (t). Impulse exerted on an object is equal to the momentum change of the object. Impulse is a vector quantity.

Formula of impulseImpulse is the product of force and time.Impulse = F tImpulse = momentum changeImpulse = mv muImpulsive ForceImpulsive force is defined as the rate of change of momentum in a reaction.It is a force which acts on an object for a very short interval during a collision or explosion.

Effects of impulse vs Force A force determines the acceleration (rate of velocity change) of an object. A greater force produces a higher acceleration. An impulse determines the velocity change of an object. A greater impulse yield a higher velocity change.Examples Involving Impulsive Force Playing football Playing badminton Playing tennis Playing golf Playing baseballLong Jump

1. The long jump pit is filled with sand to increase the reaction time when atlete land on it.2. This is to reduce the impulsive force acts on the leg of the atlete because impulsive force is inversely proportional to the reaction time.High Jump

(This image is licenced under the GNU Free Document Licence. The original file is from the Wikipedia.org.) During a high jump, a high jumper will land on a thick, soft mattress after the jump. This is to increase the reaction time and hence reduces the impulsive force acting on the high jumper.JumpingA jumper bends his/her leg during landing. This is to increase the reaction time and hence reduce the impact of impulsive force acting on the leg of the jumper.Crumble ZoneThe crumple zone increases the reaction time of collision during an accident.This causes the impulsive force to be reduced and hence reduces the risk of injuries.

Seat Belt

Prevent the driver and passengers from being flung forward or thrown out of the car during an emergency break.

Airbag

The inflated airbag during an accident acts as a cushion to lessen the impact when the driver flings forward hitting the steering wheel or dashboard.

Head RestReduce neck injury when driver and passengers are thrown backwards when the car is banged from backward.

WindscreenShatter-proof glass is used so that it will not break into small pieces when broken. This may reduce injuries caused by scattered glass.

Padded DashboardCover with soft material. This may increases the reaction time and hence reduce the impulsive force when passenger knocking on it in accident.

Collapsible Steering ColumnsThe steering will swing away from drivers chest during collision. This may reduce the impulsive force acting on the driver.

Anti-lock Braking System (ABS)Prevent the wheels from locking when brake applied suddenly by adjusting the pressure of the brake fluid. This can prevents the car from skidding.

BumperMade of elastic material so that it can increases the reaction time and hence reduces the impulsive force caused by collision.

Passenger Safety CellThe body of the car is made from strong, rigid stell cage.This may prevent the car from collapsing on the passengers during a car crash.Gravitational Field

A gravitational field as a region in which an object experiences a force due to gravitational attraction.

Gravitational Field StrengthThe gravitational field strength at a point in the gravitational field is the gravitational force acting on a mass of 1 kg placed at that point.The unit of gravitational field strength is N/kg.The gravitational field strength is denoted by the symbol "g".

Gravitational Field Strength Formula

Gravitational AccelerationThe gravitational acceleration is the acceleration of an object due to the pull of the gravitational force.The unit of gravitational acceleration is ms-2Gravitational acceleratio is also denoted by the symbol "g".Symbol: g

Important notes: Gravitational acceleration does not depend on the mass of the moving object. The magnitude of gravitational acceleration is taken to be 10ms-2. Gravitational Field Strength vs. Gravitational Acceleration Both the gravitational field strength and gravitational acceleration have the symbol, g and the same value (10ms-2) on the surface of the earth. When considering a body falling freely, the g is the gravitational acceleration. When considering objects at rest, g is the Earths gravitational field strength acting on it.Weight

The weight of an object is defined as the gravitational force acting on the object.The SI unit of weight is Newton (N)

Differences between Weight and MassWeightMass

Depends on the gravitational field strengthIndependent from the gravitational field strength

Vector quantityScalar Quantity

Unit Newton (N)Unit: Kilogram (kg)

Free Falling1. Free falling is a motion under force of gravity as the only force acting on the moving object.2. Practically, free falling can only take place in vacuum.

Gravitational Acceleration1. The gravitational acceleration is the acceleration of an object due to the pull of the gravitational force. It has the unit of ms-22. The symbol of gravitational acceleration is " g ".3. Gravitational acceleration does not depend on the mass of the moving object.4. The magnitude of gravitational acceleration is taken to be 10ms-2.Gravitational Field Strength vs. Gravitational Acceleration1. Both the gravitational field strength and gravitational acceleration have the symbol, g and the same value (10ms-2) on the surface of the earth.2. When considering a body falling freely, the g is the gravitational acceleration.3. When considering objects at rest, g is the Earths gravitational field strength acting on it.Vector and Scalar Quantity

A scalar quantity is a quantity which can be fully described by magnitude only.A vector quantity is a quantity which is fully described by both magnitude and direction.

Vector Diagram

The arrow shows the direction of the vector.The length representing the magnitude of the vector.

Equal Vector

Two vectors A and B may be defined to be equal if they have the same magnitude and point in the same direction.Case of Free Falling 1 - Falling from High Place

When an object is released from a high place,1. its initial velocity, u = 0.2. its acceleration is equal to the gravitational acceleration, g, which taken to be 10ms-2 in SPM.3. the displacement is the of the object when it reaches the ground is equal to the initial height of the object, h.Case of Free Falling 2 - Launching Object Upward

If an object is launched up vertically,1. the acceleration = -g (-10ms-2)2. the velocity become zero when the object reaches the highest point.3. the displacement of the object at highest point is equal to the vertical height of object, h4. the time taken for the object to move to the maximum height = the time taken for the object to fall from the maximum point to its initial position.Vector Addition - Triangle Method

Join the tail of the 2nd vector to the head of the 1st vector. Normally the resultant vector is marked with double arrow.

Vector Addition - Parallelogram Method

Join the tail of the 2nd vector to the tail of the 1st vector. Normally the resultant vector is marked with double arrow.

Addition of 2 Perpendicular Vectors

If 2 vectors (a and b) are perpendicular to each others, the magnitude and direction of the resultant vector can be determined by the following equation.

Vectors in Equilibrium

When 3 vectors are in equilibrium, the resultant vector = 0. After joining all the vectors tail to head, the head of the last vector will join to the tail of the first vector.

Forces in equilibrium

Forces are in equilibrium means the resultant force in all directions are zero.When the forces acting on an object are balanced, they cancel each other out. The net force is zero.

Effect : an object at rest is continuely at rest [ velocity = 0] a moving object will move at constant velocity [ a = 0]

Work1. Work done by a constant force is given by the product of the force and the distance moved in the direction of the force.2. The unit of Nm(Newton metre) or J(Joule).3. Work is a scalar quantity.Equation of Work

When the direction of force and motion are same, = 0o, therefore cos = 1Work done,W = F s

Work Done Against the Force of Gravity

Relationship between Energy and Work Done During a conversing of energy,Amount of Work Done = Amount of Energy Converted

ExampleA trolley of 5 kg mass moving against friction of 5 N. Its velocity at A is 4ms-1 and it stops at B after 4 seconds. What is the work done to overcome the friction?Answer:In this case, kinetic energy is converted into heat energy due to the friction. The work done to overcome the friction is equal to the amount of kinetic energy converted into heat energy, hencePowerPower is the rate at which work is done, which means how fast a work is done.

Formula:

EfficiencyThe efficiency of a device is defined as the percentage of the energy input that is transformed into useful energy.

Air Conditioner1. Switch off the air conditioner when not in use.2. Buy the air conditioner with suitable capacity according to the room size.3. Close all the doors and windows of the room to avoid the cool air in the room from flowing out.Refrigerator1. Always remember to close the door of refrigerator.2. Open the refrigerator only when necessarily.3. Always keep the cooling coil clean.4. Defrost the refrigerator regularly.5. Choose the refrigerator with capacity suitable for the family size.6. Refrigerator of large capacity is more efficient compare with refirgerator of small capacity.Lamp or Light Bulb1. Use fluorecent bulb rather than incandescent bulb. Fluorescent bulbs are much more efficient than incandescent bulbs.2. Use a lamp with reflector so that more light is directed towards thr desirable place.Washing Machine1. Use front-loading washing machine rather than top-loading wahing machine because it uses less water and electricity.2. Use washing machine only when you have sufficient clothes to be washed. Try to avoid washing small amount of clothes.ElasticityElasticity is the ability of a sub-stance to recover its original shape and size after distortion.Forces Between Atoms

The intermolecular forces consist of an attractive force and a repulsive force. At the equilibrium distance d, the attractive force equal to the repulsive force. If the 2 atoms are brought closer, the repulsive force will dominate, produces a net repulsive force between the atoms. If the 2 atoms are brought furhter, the attractive force will dominate, produces a net attractive force between the atoms.Graph of Forces Between 2 atoms

x0 = Equilibrium Distance

When the particles are compressed, x < x0, the attractive force between the particles increases.If the distance x exceeds the elastic limit, the attractive force will decreases.Hooke's LawHooke's Law states that if a spring is not stretched beyond its elastic limit, the force that acts on it is directly proportional to the extension of the spring.

Elastic LimitThe elastic limit of a spring is defined as the maximum force that can be applied to a spring such that the spring will be able to be restored to its original length when the force is removed.

Equation derived from Hooke's LawFrom Hook's Law, we can derived that

Spring Constant

Spring constant is defined as the ratio of the force applied on a spring to the extension of the spring.It is a measure of the stiffness of a spring or elastic object.

Graph of Streching Force - Extension

Gradient = Spring constantArea below the graph = Work done

F-x graph and spring constant

The higher the gradient, the greater the spring constant and the harder (stiffer) spring.For example, the stiffness of spring A is greater than spring B.

Spring

Arrangement in series:Arrangement in parallel:

Extension = x number of springStiffness decreasesSpring constant = k/number of springExtension = x number of springStiffness increasesSpring constant = k number of spring

Factors Affecting the Stiffness of SpringStifferLess stiff

Material type of spring(A steel spring is stiffer than a copper spring)

Diameter of wire of spring(The greater the diameter of the wire, the stiffer the spring)

Diameter of the spring(The smaller the diameter of spring, the stiffer the spring)

Length of the string(Shorter spring is stiffer)