Question

A rotating body has angular momentum $L$. If its frequency of rotation is halved and rotational kinetic energy is doubled, its angular momentum becomes

• A. $2L$
• B. $\frac{L}{4}$
• C. $4L$
• D. $\frac{L}{2}$

Hint:

Angular momentum and rotational kinetic energy are related through moment of inertia and angular velocity.

Answer 1

The Correct Option is C

Step 1: Angular momentum and rotational kinetic energy.
The angular momentum of a rotating body is given by:
\[ L = I \omega \] where $I$ is the moment of inertia and $\omega$ is the angular velocity.
The rotational kinetic energy is:
\[ K = \frac{1}{2} I \omega^2 \]
Step 2: Effect of change in frequency.
When the frequency is halved:
\[ \omega' = \frac{\omega}{2} \] Thus, the new angular momentum is:
\[ L' = I \omega' = I \times \frac{\omega}{2} = \frac{L}{2} \] However, since the kinetic energy is doubled, the increase in energy is due to the increase in inertia, which compensates for the decrease in $\omega$. Thus, angular momentum increases to $4L$.

Step 3: Conclusion.
The angular momentum becomes $4L$.