Question

State and explain the law of conservation of linear momentum.

Answer 1

The law of conservation of linear momentum

1. The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.
2. Conservation of linear momentum, the general law of physics according to which the quantity called momentum that characterizes motion never changes in an isolated collection of objects; that is, the total momentum of a system remains constant.
3. The conservation of linear momentum formula mathematically expresses the momentum of the system remains constant when the net external force is zero.
   Initial momentum $\left({\mathrm{p}}_{\mathrm{i}}\right)$ = Final momentum $\left({\mathrm{p}}_{\mathrm{f}}\right)$
4. The law of conservation of momentum can be explained by the second law of motion.
5. Newton’s second law of motion says that the rate of change of linear momentum of a body is equal to the net external force applied to it.
6. For example two bodies of mass M and m, one at rest and the other moving towards it with some velocity. If they collide and move together after the collision, we have to find the velocity of the system and the momentum will be conserved i.e., the momentum remains the same.

Mathematically it is expressed as:

If $\mathrm{p}$ is the linear momentum, $\mathrm{m}$ is the mass, and $\mathrm{v}$ is the velocity of the object, then:

$\begin{array}{l}\frac{dp}{dt}=\frac{\left(mv\right)}{dt}\\ \\ =m\frac{dv}{dt}\end{array}$

$F_{net}\mathit{=}\mathit{}m\mathit{.}a$

If the net external force acting on a body is zero, then the rate of change of momentum is also zero, which means that there is no change in momentum.