Laws of Motion

Force – A push or a pull applied on any object is called a force. Force is basically a physical
quantity which is able to either change the state of motion of the object or the size of the
object or the direction of the object. SI unit of force is Newton (N). It is vector quantity.

Properties of force-

∙ Forces applied in same

direction are always
added.
∙ Forces applied in
opposite direction are
always subtracted.
∙ The object always
moves in the direction
of the greater force.

Balanced and Unbalanced forces

The forces are said to be balanced if net force acting on the object in all directions is zero. If
the net force acting on an object is not zero then it is called as unbalanced force.

Inertia – The inability of an object to change its state of motion or direction on its own. It is
a physical quantity that enables an object to resist any change in its state of motion or
direction. Mass is the measure of inertia. Greater is the mass greater is the inertia.
Inertia of rest – The inability of an object to change its state of rest on its own is called
inertia of rest.

Inertia of motion – The inability of an object to change its state of motion on its own is
called inertia of motion.
Inertia of direction – The inability of an object to change its state of direction on its own is
called inertia of direction.

Inertia
start to fall down direction.
3. When a mat is hit with a 2. If we lie on of a moving
stick the dust particles fall bus and stop immidiately we
down tend to fall in formward
direction

Inertia
of

Inertia of Rest
Eg -
1. When a bus starts to move Direction Eg -
suddenly the passenger Inertia of Motion 1. If we suddenly turn a car
present inside the bus are in left direction the
pushed in backward direction Eg -
passengers tend to fall in
1. When brakes are applied
2. When we shake the right side.
suddenly to stop a moving
branches of a tree the leaves
bus passenger fall in forward

Newton’s First Law of Motion states that any object in a state of uniform motion or rest
remains in the state of uniform motion or rest until and unless an external unbalanced
force is applied. This law is also called as the Law of Inertia.

Mathematically –

If Fext = 0, then v = u

Physical significance of the First Law of Motion is that this law defines the concept of
force.

Suppose a car is moving with a constant speed on a straight road. In this case the engine is
applying a force on a car still the acceleration is zero. The force applied by the engine is
getting balanced by the force of friction, therefore net force on the car is zero and it is the
condition of balanced force.

Momentum –

The amount of motion contained in an object is defined as momentum. It is calculated as the

product of mass and velocity of the object. It is a vector quantity. SI unit is kg ms-1or kg m/s

⃗⃗

Questions for practice

Q1 – If the object of mass 10kg follows the following path Calculate the momentum
after 5 seconds of journey. (550 kgm/s)

Q2 – If the object of mass 10kg follows the following path Calculate the change in
momentum after from 2 to 8 seconds of journey. (-120 kgm/s)

SQ1 – If the velocity of the object is doubled keeping the mass constant, what will be the %
change in momentum?

Ans – Let the mass of the object be m and velocity be v

Original Momentum p1 = mv

New velocity = 2v
New Momentum p2 = m2v = 2mv = 2p1

The momentum doubles

Change = | New – Original |

Change = | 2mv – mv | = mv

% Change =

% Change =

Question for practice

Q3 – If the velocity of the object is halved keeping the mass constant, what will be the
% change in momentum? (50%)

Q4 – If the velocity of the object is doubled and the mass is halved, what will be the %change
in momentum? (0%)

Q5 – If the velocity of the object is tripled and mass is doubled, what will be the % change in
momentum? (500%)

Newton’s Second Law of Motion –

The second law of motion states that the rate of change of momentum w.r.t time directly
proportional to the external unbalanced forced applied.

Mathematically
 ()

Physical significance of the Second Law of Motion is that this law tells how to measure
the force.

Connected motion – A type of motion in which two objects are connected to each other

Free
Body diagrams –
ma = mg – T ------- (1)

Ma = T --------(2)

ma = mg – Ma

()

Q Calculate the total acceleration of the system for the following diagram –
()
()

()()
()
()

Find the mass of the central object such that whole system remains at rest. The angle formed
by the two ropes with central object is equal

For what mass of X will the following system have an acceleration of a in downward
direction –
Impulse = When a large force is applied for a very short interval of time, the physical
quantity produced is called as impulse.

Physical Significance –

Impulse changes the momentum of the object in a very short interval of time.

()

Real life applications of Second Law of Motion –

∙ A cricketer when catches a ball moves his hands in the direction of the movement of
the ball to increase the time of change of momentum. Since force is inversely
proportional to time, less force is required to stop the ball as the momentum of the
ball changes gradually and hence the player does not get injured.
∙ When we get down of a moving bus we need to run a few steps in the direction of the
moving bus to increase the time of change of momentum. Since force is inversely
proportional to time, less force is experienced by us and we do not fall.
∙ The crockery or tangible objects are packed in a bubble wrapped sheet to increase the
time of change of momentum when it falls on the ground. Since force is inversely
proportional to time, less force is applied by the ground on the article which prevents
 it from breaking.

Newton’s Third law of Motion – It states that every action has an equal and opposite
reaction. Action and reaction occur at the same time but on two different objects.

Mathematically

()

Real life examples of Newton’s 3rd law of motion –

∙ While jumping we push the earth down and the earth pushes us upwards. The
movement of earth is not visible as the acc. is inversely proportional to mass hence
the earth does not appear to move. It is similar to movement of rocket.
∙ While walking we push the earth backwards and the earth pushes us forward. ∙ Recoil of
a gun – when the bullet is fired from a gun, a force is applied by the hammer on the
bullet. An equal amount of force is applied by the bullet back which causes the gun to
move in backward direction.
∙ Getting down a boat – we push the boat in backward direction which pushes us in
forward direction.

Walking is an example of resolution of vectors

If we take the angle made by foot with the ground as
then Resolving the normal reaction R into rectangular
components

remains unbalanced which

enables us to walk.

Prove that the second law of motion is the real law of motion –

Proof of first law –

 , the object at rest remains at rest or the object in uniform motion remains in same
state of motion until and unless an ext. unbalanced force is applied

Proof of third –

Force applied by A on B = FAB

Force applied by B on A = FBA

Total force = F = FAB + FBA

Since the system is isolated, there is no external force applied on

the object
F=0
FAB + FBA = 0
FAB = - FBA

Apparent weight of the object in lift –

In case a) R = mg, the weight shown in weighing balance is equal to actual weight.

In case b) ma = R – mg, R = mg + ma, the weight shown in weighing balance is greater than
actual weight.

In case c) ma = mg – R, R = mg – ma, the weight shown in weighing balance is lesser than

actual weight.

In case d) mg = mg – R, R = 0, the weight shown in weighing balance is equal to zero. The

object experiences weightlessness.

Why is it difficult to push but easier to pull?

In the case of pulling

R + F sin x = mg
R = mg – F sin x
therefore the net weight of the object
decreases.

In the case of pushing

R = F sin x + mg
therefore the net weight of the object
increases

Hence the pushing is difficult than pulling.

Conservation of momentum states that total momentum of the system is conserved. The total
momentum before the event and after the event is always same.

3rd

( )

Q Calculate the velocity by which A and B will move after A strikes B.

Resolving v1and v2 into their rectangular

components

Along x axis
()

By conservation of momentum

Along y axis
()
By conservation of momentum

m/s
√ m/s
Q – A ball of mass M kept stationery at a point suddenly explodes into 3 equal parts such that
two parts move at an angle of 90oto each other with equal velocities. Find out the magnitude
and direction of the velocity by which the third part should move.

Q – A ball of mass M kept stationery at a point suddenly explodes into 3 equal parts such that
two parts move at an angle of 120oto each other with velocities 3m/s and 5m/s. Find out the
magnitude and direction of the velocity by which the third part should move?

Friction - Friction is a force which opposes relative motion. Friction is a self-adjusting force.
Types of friction –

∙ Static Friction – The force of friction which is applied on any object when it is at rest.
Limiting Friction – The maximum value of static friction is called as limiting friction.
The force of static friction applied on the object just before it is about to move.
∙ Kinetic Friction – The force of friction which is applied on any object when it is in
motion.
a. Rolling friction – The force of friction which is applied on any object rolls over
another object/surface.
b. Sliding friction – The force of friction which is applied on any object slides over
another object/surface.

Laws of friction

1. The force of friction is directly proportional to normal reaction ‘R’.

. (-ve) indicates that the direction of force of friction is in opposite to the direction of
motion at the point of contact.
2. Force of friction is always in opposite direction of motion of the object at the point of
contact.
3. Coefficient of friction is independent of area of contact.
Angle of friction – The angle formed between the Normal reaction R and resultant of normal
reaction R and force of friction.

Coefficient of friction is numerically equal to tangent of angle of friction

Angle of repose – The angle formed by the

inclined surface with the horizontal is
called angle of repose.

Coefficient of friction is numerically equal to tangent of angle of repose

If the object slides down

If the object remains at rest

Why rolling friction is less that sliding

friction?
Ans – if we look at the diagram given then
at the point of contact with the ground of
the wheel, the direction of motion is
towards left, hence the force of friction is
towards right supporting the motion of the
object.

Object around a turn

A centripetal force is required by the objects at turn

which is provided by the force of friction between the
ground and the tyres.

The velocity of the object should either be √ √

In rain the value of decreases hence the vehicles slips as the maximum velocity allowed dec

Banking of roads – the roads in hilly areas are not flat

but elevated by a very small angle in order to avoid
slipping of the objects

∙ when friction is not included

∙ When friction is included

()

()
()()

()
 ()

()
()

√[ ]

Bending of a cyclist –

When the cyclist bends at an angle with the

horizontal
the force of friction increases and the person does
not slip.

Greater is the angle greater is coefficient of friction.