Question

Establish a relation between torque and angular momentum for a system of particles.
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Answer 1

Answer:

Relation between Torque and Angular Momentum

As we know, l = r × p, differentiating on both the sides,

->> dl / dt = d / dt ( r × p)

->> dl /dt = dr/dt × p + r × dp /dt

->> dl / dt = v × p + r × dp / dt

->> dl / dt = v × mv  + r × dp / dt

since, v = 0

->> dl / dt =  r × dp / dt = r × F = τ

⇒ dl  / dt = τ

>>  So the time rate of change of angular momentum is equal to torque. So finally we can say that rate of change of angular momentum is equal to the torque acting on it. The angular momentum of the system of a particle is denoted by :

Explanation:

Hence,

L = l1 +  l2 + …..ln

This can be written as Σ =( li ). Now we know that l = r × p, so

( li ) = ri × pi

The total angular momentum of the system is Σ( ri × pi)

I hope it helps.