Question

derive torque is equal to dL by dt​

Answer 1

Note that since F = dp/dt, the time rate of change of linear momentum, you should notice the angular equivalent of the expression for torque, i.e. T = dL/dt, the time rate of change of angular momentum. Torque is the "force equivalent" in rotational motion.

Answer 2

Answer:

Explanation:

We know that, dldt = τ, a total torque of the system will be the summation of each of the particles.

Σ dldt

τi  = ri × Fi

Σ =  ri × Fi

Torque is external as well as internal.

τ = τext  + τint

τext  =  Σ  ri × Fiext

τin =  Σ  ri × Fiint

So here if internal force becomes zero,

τext  =  dldt

Hence we can say that time rate of the total angular momentum of the system of particles about a point is equal to the sum of the external torques acting on the system taken about the same point.