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)