Question

A uniform circular disc of mass 2 kg and radius 0.5 m is mounted on a frictionless axle. A force of 4 N is applied tangentially at the rim for 2 seconds. Find the angular velocity acquired by the disc at the end of 2 seconds.

• A. 8 rad/s
• B. 10 rad/s
• C. 12 rad/s
• D. 16 rad/s

Hint:

When calculating the work done on a rotating object, equate the work to the change in rotational kinetic energy.

Answer 1

The Correct Option is D

The work done on the disc is: \( W = F \cdot d = 4 \times 2 \pi \times 0.5 = 4 \pi \, \text{J} \).
This work is also equivalent to the change in rotational kinetic energy: \( K = \frac{1}{2} I \omega^2 \).
For a solid disc, \( I = \frac{1}{2} m r^2 \), therefore: \( K = \frac{1}{2} \times \frac{1}{2} \times 2 \times (0.5)^2 \times \omega^2 = \frac{1}{4} \times \omega^2 \).
Equating the work and kinetic energy: \( 4 \pi = \frac{1}{4} \times \omega^2 \).
Solving for \( \omega \) yields: \( \omega = 16 \, \text{rad/s} \).
The disc thus acquires an angular velocity of \( 16 \, \text{rad/s} \).