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# what is the principle of conservation of momentum?

Apoorva Arora IIT Roorkee
7 years ago
In a closed system (one that does not exchange any matter with the outside and is not acted on by outside forces) the total momentum is constant. This fact, known as the law of conservation of momentum, is implied by Newton's laws of motion. Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second law states that F1 = dp1/dt and F2 = dp2/dt. Therefore
$\frac{\mathrm{d} P_{1}}{\mathrm{d} t}=-\frac{\mathrm{d} P_{2}}{\mathrm{d} t}$
$\frac{\mathrm{d} (P_{1}+P_{2})}{\mathrm{d} t}=0$
If the velocities of the particles are u1 and u2 before the interaction, and afterwards they are v1 and v2, then
$m_{1}u_{1}+m_{2}u_{2}=m_{1}v_{1}+m_{2}v_{2}$.
Thanks and Regards
Apoorva Arora
IIT Roorkee