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Q.
The angular momentum of a rotating body changes from $ {{A}_{0}} $ to $ 4{{A}_{0}} $ in $4$ min. The torque acting on the body is:
BHUBHU 2005System of Particles and Rotational Motion
Solution:
The rate of change of angular momentum (dJ) of a body is equal to the external torque $ (\tau ) $ acting upon the body.
Torque = rate of change of angular momentum or
$ \tau =\frac{dJ}{dt} $
Given, $ dJ=4{{A}_{0}}-{{A}_{0}},dt=4\text{ }\min $
$ \therefore $ $ \tau =\frac{3}{4}{{A}_{0}} $
This formula $ \frac{dJ}{dt} $ is similar to the formula for linear motion.