## Momentum of a Body

The momentum of a body is the quantity of motion in it. It depends on two things

1. The mass of the object moving (m),

2. The velocity with which it is moving (V).

Momentum is the product of mass and velocity. It is denoted by P.

P = m V

Momentum is a vector quantity an its direction is the same as that of the velocity.

**Unit of Momentum**

Momentum = mass x velocity

= kg x m/s

= kg x m/s x s/s

= kg x m/s2 x s

since kg. m/s2 is newton (N)

momentum = N-s

Hence the S.I unit of momentum is N-s.

**Unbalanced or Net Force is equal to the Rate of Change of Momentum**

*i.e., F = (mVf = mVi) / t*

**Proof**

Consider a body of mass ‘m’ moving with a velocity Vl. A net force F acts on it for a time ‘t’. Its velocity then becomes Vf.

Therefore

Initial momentum of the body = m Vi

Final momentum of the body = m Vf

Time interval = t

Unbalanced force = F

Therefore

Rate of change of momentum = (m Vf – m Vi) / t ………………….. (1)

But

(Vf – Vi) / t = a

Therefore,

Rate of change of momentum = m a = F ………………… (2)

Substituting the value of rate of change of momentum from equation (2) in equation (1), we get

F = (m Vf – m Vi) / t ……………………….. Proved

Newton’s Third Law of Motion Next Post:

Law of Conservation of Momentum