Question

Show that the time rate of change of the angular momentum of a particle is equal to the torque acting on it

Answer 1

Consider a particle of mass m and linear momentum at a position  relative to the origin O. The angular momentum L of the particle with respect to the origin O is defined to be



Magnitude of the angular momentum vector is

L = rp sinθ

Where, p is the magnitude of and θ is the angle between and



Differentiating with respect to time,



Then, the velocity of the particle

Because of this, 

∴Equation (i) becomes



Hence, 



I'd suggest you to properly go through the study material. The same has been explained there.