Question

Obtain the relation between torque and angular momentum

Answer 1

Rate of change of angular momentum is equal to torque. Torque simply speaking is the measure of change in angular momentum of an object with respect to time. This is analogous to force in linear motion which is the measure of change in linear momentum with respect to time. Torque(T)=dL/dt (where L is angular momentum).

Answer 2

Hey !!

We know that,

Torque,           τ = r × F

Angular momentum,     L = r × p

On differentiating both sides w.r.t time t, we get

         dL/dt = d/dt (r × p) = dr/dt × p × r × dp/dt

          = v × p + r × F                      [∴ dp/dt = F]

            = 0 + τ

∵              τ = dL/dt

Thus, the torque acting on a particle is equal to its rate of change of angular momentum.

Good luck !!