Question

Discuss conservation of angular momentum with example.

Answer 1

When no external torque acts on the body, the net angular momentum of a rotating rigid body remains constant. This is known as the law of conservation of angular momentum.

τ = ${\displaystyle \frac{\text{dL}}{\text{dt}}}$

If τ = 0 then, L = constant.

As the angular momentum is L = Iω, the conservation of angular momentum could further be written for initial and final situations as,
I_iω_i = I_iω_i (or) Iω = constant

The above equations say that if I increase ω will decrease and vice – versa to keep the angular momentum constant.

conservation of angular momentum for ice dancer

There are several situations where the principle of conservation of angular momentum is applicable. One striking example is an ice dancer as shown in Figure A. The dancer spins slowly when the hands are stretched out and spins faster when the hands are brought close to the body.

Stretching of hands away from body increases moment of inertia, thus the angular velocity decreases resulting in a slower spin. When the hands are brought close to the body, the moment of inertia decreases, and thus the angular velocity increases resulting in a faster spin. A diver while in the air as in Figure B curls the body close to decrease the moment of inertia, which in turn helps to increase the number of somersaults in the air.

 

conservation of angular momentum for a diver