# Conservation of Momentum Explained in Detail

What is the conservation of momentum? How is it represented in the form of an equation? Read to get all the answers.

Omkar Phatak

Last Updated: Mar 8, 2018

What is Momentum?

Momentum of a particle or a body is the product of its velocity and mass. Momentum is a vector quantity as it is a product of a scalar (mass) and a vector (momentum). Its formula is as follows:

Where M is mass and V is the velocity of the particle. The SI unit of momentum is 'Kg.m/s'.

**P = MV**Where M is mass and V is the velocity of the particle. The SI unit of momentum is 'Kg.m/s'.

Definition

The principle of conservation of momentum states that '

where ΔP

*In any closed system, with no external forces acting, the total momentum of the system does not change.*' This could be alternatively stated as 'The vector sum of all momenta, in a closed system, unaffected by external forces, is zero.' The principle is a consequence of Newton's first law of motion. When two bodies in an isolated system collide, their total momentum before collision is equal to their total momentum after collision. This can be stated as:**ΔP**_{1}+ ΔP_{2}= 0where ΔP

_{1}is the change in momentum of the first particle, while ΔP_{2}is the change in momentum of the second particle.Equation

The equation is stated as follows. For a collision between two particles in an isolated system, the total momentum before and after collision is constant.

Here M

**M**_{1}U_{1}+ M_{2}U_{2}= M_{1}V_{1}+ M_{2}V_{2}Here M

_{1}is the mass of the first particle, M_{2}is the mass of the second particle, U_{1}is initial velocity of first particle, U_{2}is initial velocity of the second particle, and V_{1}and V_{2}are the final velocities of the first and second particles respectively.Examples

Examples of conservation of linear momentum abound in everyday life. Wherever there is collision, the conservation principle is at work. For example, when a baseball collides with the bat, the sum of the initial momenta and sum of the final momenta of bat and ball, remain the same. Whatever momentum the bat loses, the baseball gains.