# Momentum

If you have played cricket, you would have experienced that catching a ball which is moving with a higher velocity is more difficult than catching a ball which is moving with lesser velocity. Similarly, it is easier to catch a table tennis ball as compared to a cricket ball when both are dropped from the same height. Thus, we see that moving bodies postess a physical quantity associated with their motion which determine how much force is required to bring them to rest . This quantity which depends on the mass and velocity of the moving body is called momentum and is defined as momentum (p) = mass (m) × velocity (v)

 NOTE Since mas is a scalar and velocity is a vector, momentum is a vector quantity. If a body is moving along a straight path, the body is said to post linear momentum.

Definition of momentum – The momentum of a system is conserved ( does not change) when there is no net external force.

## Units of Momentum

Si unit of momentum is kg m s-1 or Newton

Cgs unit of momentum is g cm s-1

EXAMPLE

The speeds of a rabbit and a hare are 10 m s-1 and 25 m s-1, respectively. The mass of the hare is 15 kg and that of the rabbit is 50 kg. Which of the two has greater momentum ?

( Assume speed of each to be steady.)

SOLUTION

We have seen above that, momentum = mass × velocity

Velocity being a vector quantity has both magnitude and direction . In the question , only the magnitude of velocity, i.e., speed, is given. There is no information regarding the direction of motion of the hare and the rabbit. Since it is not possible to compare two vectors , it is not possible to compare their momenta. However, we can compare the magnitudes of their momenta as below:

Mass of rabbit = 50 kg

Speed ​​of rabbit = 10 m s-1

`Ptortoise = 10 × 2 = 20 kg m s-1`

Mass of the hare = 15 kg

Speed ​​of the hare = 25 m

`Phare = 3 × 5 = 15 kg m s-1`

Thus, the magnitude of momentum of the rabbit is greater than that of the hare.

Low of conservation of momentum – the total momentum of a system of bodies remains constant unless there is a net external force acting on the system.

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