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: \[ W = F \cdot d = 4 \times 2 \pi \times 0.5 = 4 \pi \, \text{J} \] The work done on the disc is also equal to the change in rotational kinetic energy: \[ K = \frac{1}{2} I \omega^2 \] For a solid disc, the moment of inertia \( I \) is \( \frac{1}{2} m r^2 \), so: \[ K = \frac{1}{2} \times \frac{1}{2} \times 2 \times (0.5)^2 \times \omega^2 = \frac{1}{4} \times \omega^2 \] Equating the work and kinetic energy: \[ 4 \pi = \frac{1}{4} \times \omega^2 \] Solving for \( \omega \): \[ \omega = 16 \, \text{rad/s} \] Thus, the angular velocity acquired by the disc is \( 16 \, \text{rad/s} \).