Question

State and explain the law of conservation of linear momentum.

Answer 1

Hint: The linear momentum of a system is conserved in absence of external force. Assume a system with several particle and sum of momentum of each particle is equal to the net
momentum of the system and use Newton’s second law of motion.

Complete step by step answer:
The Newton’s second law and his third law leads to the one of the fundamental and major
principle called law of conservation of momentum.

According to the law of conservation of momentum, when no external force is applied on the
the system consists of several particles; the net linear momentum is conserved. The net linear
momentum of the system is the vector sum of the linear momenta of the particles in the
System.

Let us consider a system on which there is no external force is acting and it consists of n
number of particles have masses ${m_1}$, ${m_2}$, ${m_3}$ and so on that are in motion with
velocity ${v_1}$, ${v_2}$,... so on.
The net linear momentum of the system is calculated as,
$
\vec p = {m_1}{{\vec v}_1} + {m_2}{{\vec v}_2} + ..... + {m_n}{{\vec v}_n}\\
= {{\vec p}_1} + {{\vec p}_2} + ..... + {{\vec p}_n}
$
From the Newton’s law of motion, if $\vec F$ is the external force on the system, then
$\vec F = \dfrac{{d\vec p}}{{dt}}$

Since there is no force acting on the system, so,
$0 = \dfrac{{d\vec p}}{{dt}}$

We know that the derivative of a constant is equal to zero.
$\vec p = $constant

Or we can also write the above equation as,
${\vec p_1} + {\vec p_2} + ...... + {\vec p_n} = $constant

Thus, when no external force is applied on the system consists of several particles; the net
linear momentum is conserved. This is known as the law of conservation of momentum.

Note: Conservation of linear momentum can be explained by the concept of collision.
 The linear momentum of a system before collision is equal to the linear momentum.