Question

A disc starts rotating from rest with constant acceleration and attains angular velocity of 20 rad/s in 5 seconds. The total angular displacement during this interval is

• A. 50 rad
• B. 100 rad
• C. 200 rad
• D. 400 rad

Hint:

Use rotational kinematics: $\theta = \omega_0 t + \dfrac{1}{2} \alpha t^2$ when angular acceleration is constant.

Answer 1

The Correct Option is A

Given: initial angular velocity $\omega_0 = 0$, final $\omega = 20$ rad/s, $t = 5$ s
Angular displacement $\theta = \omega_0 t + \dfrac{1}{2} \alpha t^2$
First find angular acceleration: $\alpha = \dfrac{\omega - \omega_0}{t} = \dfrac{20 - 0}{5} = 4$ rad/s$^2$
Now compute displacement: $\theta = 0 + \dfrac{1}{2} \times 4 \times 5^2 = 2 \times 25 = 50$ rad