THE LAWS OF MOTION,
BY SWAPNEEL BHATT
What are Newton’s Laws of Motion ?
• These are three physical laws that state the relationship of a objector a body
with the forces acting on it.
• The first law - An object at rest remains at rest unless acted upon by a force.
An object in motion remains in motion, and at a constant velocity, unless
acted upon by a force.
• The second law - The acceleration of a body is directly proportional to, and
in the same direction as, the net force acting on the body, and inversely
proportional to its mass. Thus, F = ma, where F is the net force acting on the
object, m is the mass of the object and a is the acceleration of the object .
• The third law - When one body exerts a force on a second body, the second
body simultaneously exerts a force equal in magnitude and opposite in
direction to that of the first body.
Balanced and Unbalanced Forces
When the resultant of all the forces acting on a body is zero, then the forces are
called unbalanced forces .
These cannot change the state of rest or motion of a body .
When the resultant of all the forces acting upon a body is unequal to zero, then it is
called an unbalanced force .
These can change the state of rest or motion of a body .
Newton’s First law of Motion
There are three parts of this law:-
1. A body at rest continues to remain at rest until some external force is applied on
the body which causes it to move .
2. A body in uniform motion continues to be in uniform speed till a external force is
applied on it which causes its speed to change .
3. A body moving along a straight line will continue to move along this straight line
till an external force is applied which causes it to change its direction.
The definition of force derived from Newton’s
First Law of Motion
• This law states that that a body continues to be in a state of rest or in a
state of uniform motion along a straight line, unless an external force is
applied on the body to change the state .
• It means that force applied on a body alone can change its state of rest or
state of uniform motion along a straight line. Therefore, force may be
defined as an external effort in the form of a push or pull which
• 1. Actually moves or tries to move a body at rest
• 2. Actually stops or tries to stop a moving body
• 3. Actually changes or tries to change the direction of the body
• The First Law of Motion gives that a body on its own cannot change its state
of rest or motion along a straight line.
• Through this we derive that all objects resist a change in their state or
oppose the forces that try to change their state. This property is called
• Inertia of a body is the stability of the body to change by itself its state of
rest or state of uniform motion along a straight line . Thus, Newton’s First
Law of Motion defines Inertia and is also called the Law of Inertia .
The 3 Types of Inertia
1. Inertia of rest – The inability of a body to change by itself is the inertia of rest It
means a body at rest remains at rest and cannot start moving on its own.
2. Inertia of motion – A body in motion remains in motion and cannot stop on its
own. A body in motion opposes the which try to stop it
3. Inertia of Direction-A body moving along a straight line will continue to move
along the straight line until a external forces changes its direction. A body moving
along a straight line will oppose the forces which try to change its direction.
The impact of ,motion produced by objects depends on their mass and velocity.
Momentum of a body is the product of the mass and velocity of the body.
Momentum = Mass x velocity
If momentum =p, Mass =m, Velocity =v, then p=mv
Momentum is a vector quantity.
The SI unit of momentum is kg m/s
If mass of the body is doubled, leaving velocity unchanged, the momentum will
also double. This is true vice-versa also.
If Mass and Velocity are both doubled, momentum will increase by 4 times .
Impulsive force and Impulse
Impulsive force is a higher magnitude force acting for a very short time. Eg – a
cricket bat hitting a ball
Impulse is defined by the change in momentum
Impulse = final momentum minus initial momentum
I = mv – mu where I= impulse, m= mass of body, v = final velocity and u = initial
The SI unit for impulse is kg m/s
Impulse is a vector quantity
Newton’s Second law of Motion
• Newton’s second law of motion states that the rate of change of
momentum of a body is directly proportional to the external force applied
on the body.
• This change always takes place in the direction of the applied force.
• This rate of change of momentum can be obtained by dividing the change
of momentum by the time taken for the change .
• The consequence of Newton’s second law of motion is F = ma
Mathematical Formulation of the Second law of
• m = mass of a body, F = external force applied which is constant in
magnitude, t = time for which the force is applied, u = initial velocity of the
body along the straight line, v = final velocity of the body along the straight
line, after t seconds
• Initial momentum of the body =p1=mu
• Final momentum of the body = p2 = mv
• Change in momentum of the body = p2-p1= mv-mu = m(v-u) = impulse
• Rate of change of momentum = m(v-u)/t
• However v-u/t = acceleration = a
• Therefore from this equation we derive that rate of change of momentum =
Mathematical Formation of the Second Law of
According to Newton’s second Law of motion, rate of change of momentum is directly
proportional to the force applied
i.e. ma is directly proportional to F or F is directly proportional to ma or F = kma where k is a
constant of proportionality.
If we substitute f, k, and m for 1 in the previous equation, we get the equation F = ma. This is
the mathematical form of Newton’s second law of motion.
From this we get that Force is the product of the mass and acceleration of the body
The SI unit of force is newton or n
One newton force is that much force which produces acceleration of 1m/s square in a body
of mass 1 kg
1N = 1kg x 1m/s square = 1kg m/s square
Force is a vector quantity, whose direction is the same as acceleration of the body
Newton’s Third law of Motion
Newton’s Third Law of Motion that to every action, there is always a equal and
opposite reaction, i.e. the forces of action and reaction are always equal and
These forces act on two different objects and never cancel each other.
Although the action and reaction forces are equal in magnitude, yet these forces
may not produce accelerations of equal magnitude.
This is because each force acts on a different object and may have different mass.
Law of Conservation of momentum
• When two or more bodies interact with one another, the vector sum of their
linear momenta, remains constant ( i.e., conserved ), and is not affected
due to their mutual action and reaction . The only condition is that no
external unbalanced should be acting on the system of bodies .