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A disc is rotating with angular speed $\omega$. If a child sits on it, what is conserved : -
A
Linear momentum
B
Angular momentum
C
Kinetic energy
D
Potential energy
Detailed Solution
When the child sits on the disc, the forces between the child and the disc are internal to the system. No external torque acts about the axis of rotation.
So the angular momentum $L = I\omega$ is conserved. The moment of inertia increases, so the angular speed decreases: $I_1\omega_1 = I_2\omega_2$.
Kinetic energy $\dfrac{L^2}{2I}$ decreases, because some energy is lost as the child comes to rotate with the disc (friction).
So angular momentum is conserved.
So the angular momentum $L = I\omega$ is conserved. The moment of inertia increases, so the angular speed decreases: $I_1\omega_1 = I_2\omega_2$.
Kinetic energy $\dfrac{L^2}{2I}$ decreases, because some energy is lost as the child comes to rotate with the disc (friction).
So angular momentum is conserved.