prove that the rate of change of angular momrntum of a particle is equal to da torque acting on it.

• 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 is and 

Because of this, 

∴Equation (i) becomes

Hence, 

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