INFINITY CLASSES

Important notes of LAWS OF MOTION

Force:- Force may be defined as an influence, which tend to change state, speed, direction and shape
of a body. It has both magnitude and direction and is therefore, a vector quantity.. It can also change the
shape of a body. Force is a vector quantity.

Units of force: In S.I system, force is measured in Newton’s represented by letter “N” while as in C.G.S
system its values are represented in dynes.

Effects of force:- Some of the common effects of force are:-

1. A force may move a body at rest.

2. A force may stop a moving body.

3. A force can change the speed of a body.

4. A force may change the direction of a moving body.

5. A force may change the size and shape of a body.

Forces can be classified into two classes:- 1. Contact forces 2. Non contact forces.

1.Contact force - The contact forces represent the result of physical contact between two objects, one
by which force is exerted and the other on which force is exerted e.g. pulling of a coiled spring, pulling of
a cart.

Types of Contact force -

i) Frictional force - It is a contact force that opposes the motion of a body it always opposes the moving
body and acting opposite direction of a moving body . It produce heating effect.

ii) Normal reaction force - It is a contact force that is applied by a surface to counter balance the weight
force when the object is kept on a surface. It is denoted by R. Weight and normal reaction force is equal
in magnitude but opposite in direction and net force on this system is always zero

iii) Tension force - It is a force experienced when a row wire or string is pulled by force acting from
opposite side.
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Important notes of LAWS OF MOTION

iv) Restoring force - A restoring force is a force that acts to return an object to its equilibrium position

iv ) Force due to collision - The force exerted on two body when the collide is called the
collision force .

2. Non-Contact forces-The force which do not involve physical contact between the two objects but
act through the space between the two e.g. the gravitational force, electrical force etc.

Types of Non- Contact force

I) Gravitational force - In universe each particles attract the other particle due to its mass the force of
attraction between them is called gravitational force. If one of the body is earth and the gravitational
force between the earth and any other body is called gravity

ii) Magnetic force - It is the force that comes into play due to magnetic pole it may be practice Or
repulsive in nature. Magnet has two poles not pole and the South pole . Like pole repel each other and
unlike pole attract each other.

iii) Electrostatics force - It is the force that comes into play due to electric charge it a may attarctive and
repulsive by Nature electric charge are of two types positive and negative like charges repel each other
and unlike charges attract each other.
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Important notes of LAWS OF MOTION
Types of force:- Forces are of main two types 1. BALANCED FORCE 2. UNBALANCED FORCE

(i). Balanced force:- A force is said to be balanced if the resultant of all the forces acting on a body is
equal to 0. For example: In the game of tug of war, the two teams pull each other in the opposite
directions. If the two teams pull the rope with equal force i.e. F1 = F2, then the rope does not move in
either direction. Under this condition, the forces acting on a rope are balanced forces.

(ii). Unbalanced force:- A force is said to be unbalanced if the resultant of all the forces acting on a
body is not equal to 0. For example. In the tug of war, if the force applied by a team is greater than that
applied by the other team Thus, the unbalanced forces produce motion.

Newton’s Laws of Motion

Newton derived three basic laws based on his name, to describe motion. All these laws are known as
Newton’s laws of motion0

Newton’s First Law of Motion or Galileo’s Law of Inertia:- It states that, “Everybody continues
to remains in the state of rest or motion until or unless completed by some external force to change its
state of rest or motion”. In other words, the first law of motion recognizes that everybody has some
inertia i-e the property of a body to remain in a state of rest or uniform motion. This law is accordingly
also known as, “Law of inertia”.

Ex- A cricket ball will remain in motion after hit by the player unless and until the force of friction and the
resistance of air stop it and changes its motion into rest.

Inertia:- The word inertia means unchanging. It has been derived from the Latin word inert. It is
defined as the property of a body to remain in the state of rest or uniform motion. In other words, inertia
may be defined as the property of a body to remain in the state of rest or uniform motion.

It is of three main types:-

(i). Inertia of Rest:- It is the inability of a body to change its rest or its property to remain in rest. This
means a body at rest remains at rest and cannot start moving on its own.

(ii). Inertia of Motion:- It is the inability of a body to change its state of motion or its property of a body
to remain in the same direction ∝

(iii) Inertia of direction:- It is the inability of a body to change by itself its direction of motion.

Momentum - Momentum is a fundamental concept in physics that measures an object's

motion. It is defined as the product of an object's mass and velocity, and is represented by the
formula Momentum is a vector quantity, so its direction is the same as the direction of
velocity. The SI unit for momentum is kg m/s.

𝑝=𝑚𝑣 where 𝑝 = momentum m = mass v= velocity

 INFINITY CLASSES
Important notes of LAWS OF MOTION
Second Law of Motion:- According to Newton’s second law of motion, the rate of change of linear
momentum of a body is directly proportional to the external force applied on the body, and this change
takes place always in the direction of the applied force.

Suppose m = mass of body, u = initial velocity of the body , F = an external force applied on
the body, t = time v = Final velocity of the body , after t second.

Initial linear momentum of the body, P1 = mu

Final linear momentum of the body, P2 = mv

Change in linear momentum of the body = p2 – p1 = mv – mu = m (v – u)

Rate of change of linear momentum = change in linear momentum / time taken

= m (v – u) / t ( a = v-u /t )

=mxa

Therefore from equation (i), rate of change of linear momentum = m x a

According to Newton’s second law of motion, rate of change of linear momentum α force applied
Therefore F ∝ mxa F= k m x a ( k=1) where k is constant

F= m x a
Relation between force and momentum:- Consider a body of mass (m) having an acceleration of
(a) m/sec2 .Then, the force exerted by the body (f) can be given by the relation. F = m . a ….. (i)

a = v-u/t now put the value of a in equation I then we get – F = m(v-u) / t , F = mv-mu/t

f= (final momentum – initial momentum ) / time taken , F= rate of change of momentum

Thus, from the above relation, it is clear that the force applied to a body is directly proportional to the
rate of change in momentum produced in the body, when the change in momentum takes place in the
direction of force applied. Thus, the relation of force and momentum gives another statement of the
Newton’s 2nd law of motion.

Newton’s Third Law of motion:- It states that, “If a body exerts a force on some other body, then
the second body exerts a force of some magnitude on it but in opposite direction”. Thus, in other words it
states that, “To every action there is an equal and opposite reaction”.

For example: 1. When a ball is thrown on to a wall, it comes back with the same force and speed. 2.
When we pull a spring, it pulls us back with the same force. 3. When we hit a ball to the ground, it comes
back at the same speed.

Law of conservation of momentum - Law of Conservation of Momentum states that the total
momentum of objects before and after collision remains constant. In another
words , Conservation of Momentum states that the momentum of the system is always conserved,
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Important notes of LAWS OF MOTION
i.e. initial momentum and final momentum of the system are always conserved. We can also state
that the total momentum of the system is always constant.

Derivation of Conservation of Momentum

The law of Conservation of Momentum is derived with the help of Newton’s third law of
motion which states that for every action there is an equal and opposite reaction.
Consider two point masses m1 and m2. Initially, these bodies were moving with the
velocities u1 and u2. Now they collide with each other and their final velocities become
v1 and v2. Their time of collision is t.
Now the change in momentum of the mass A △PA = m1(v1 – u1)
Now the change in momentum of the mass B △PB = m1(v2 – u2)
From Newton’s law of motion,
FAB = -FBA….(1)
We also know that, F = △P/t Thus,
FAB = △PA / t
FBA = △PB / t
Now, from (1)
△PA / t = -△PB / t
m1(v1 – u1)/t = – m1(v2 – u2)/t
m1(v1 – u1) = – m1(v2 – u2)
m1(v1 – u1) + m1(v2 – u2) = 0
m 1u1 + m 2u2 = m 1v1 + m 2v2