# Momentum

### Momentum

According to Newton’s Law of Motion, all moving bodies continue to be in the state of rest or motion unless interfered by some external force. The mass principle can be applied to momentum i.e. if the mass and velocity of an object remains same then the momentum of the object remains constant.

What is Momentum?

Momentum can be defined as MASS IN MOTION. All objects have mass, so if an object is moving, then it has momentum, it has mass in motion. The amount of momentum that an object as is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity.

The momentum of an object is equal to the momentum of the object is equal to mass of the object times the velocity of the object.

Momentum (P) = Mass (m) x Velocity (v)

The momentum is directly proportional to an object’s mass and directly proportional to the object’s velocity. The standard metric unit of momentum is the kg.m/ sec.

Example: Imagine two brothers Pranay and Vinay running in the playground. Pranay weighs 40kg and Vinay weighs 50 kg, both of them are running at the same speed in the same direction.

(a) Who has more momentum and why?

(b) Who will get hurt more if they hit a wall?

The answer to both the above two questions would be Vinay, because he has more momentum as the velocity of Pranay and Vinay is same, their momentum will depend upon their mass, therefore Vinay will have more momentum than Pranay.

The law of conservation of momentum states that the total momentum of a closed system does not change, it means that if two bodies collide with each other, their total momentum after the collision will be equal to their momentum before the collision.

How to find the Momentum?

Problem: A bike is moving at the rate of 30m/sec carrying a momentum of 5000kg.m/sec. find the mass of the bike?

Solution: Given,

Velocity (v) = 30 m/sec

Momentum (P) = 5000 kg.m/sec

We know that:

Momentum (P) = Mass (m) x Velocity (v)

$$Mass(m)\,=\,\frac{Momentum(P)}{Velocity(v)}\,=\,\frac{5000\,kg.m/\sec}{30\,m/\sec}\,=\,166.66\,kg$$

∴ Mass (m) = 166.66 kg.