Question

State and Prove the principle of conservation of angular momentum. Explain the principle of conservation of angular momentum with examples.

Answer 1

We have to prove that angular momentum of a body remains constant when external torque is zero.
e.g., L = $I\omega$ = constant

Proof : by the definition of torque, rate of change of angular momentum is called torque.
e.g., $\tau=\frac{dL}{dt}$
if $\tau=0\implies\frac{dL}{dt}=0$
And hence, L = constant

hence , it is clear that , when external torque acts on system of particles , angular momentum of system remains conserved.

e.g., $I\omega$ = constant

or, $I_1\omega_1=I_2\omega_2$

For example :- when a man with stretched out arms stands a turn table which is revolving then his moment of inertia is high. If he folded his hands . The moment of inertia decreases and hence, the angular velocity , linear velocity increase. But the period decreases. In both cases angular momentum remains conserved.
We know, angular momentum is product of moment of inertia and angular velocity.
e.g., L = $I\omega$

Answer 2

The linear momentum and angular momentum of the body is given by →p=m→v and →l=→r×→p about an axis through the origin. The angular momentum →l may change with time due to a torque on the particle. ∴→l = constant, i.e. →l is conserved. ... its angular velocity will also change if there is no external torque