Question

A flywheel starts from rest and revolves with an acceleration of \(0.5\ \text{rad/sec}^2\). What will be its angular displacement after 10 seconds?

• A. 5 radians
• B. 25 radians
• C. 35 radians
• D. 50 radians

Hint:

Use the equation of angular motion that relates displacement, initial angular velocity, angular acceleration and time.

Answer 1

The Correct Option is B

Since the flywheel accelerates uniformly from rest, we can also solve this using average angular velocity.

The final angular velocity after 10 seconds is $\omega = \omega_0 + \alpha t = 0 + 0.5 \times 10 = 5\ \text{rad/sec}$.

Because the acceleration is constant, the average angular velocity over the interval is the mean of the initial and final values: $\omega_{avg} = \frac{\omega_0 + \omega}{2} = \frac{0+5}{2} = 2.5\ \text{rad/sec}$.

Angular displacement equals average angular velocity multiplied by time: $\theta = \omega_{avg} \times t = 2.5 \times 10 = 25$ radians.

This confirms the same result through a different route.

\[\boxed{25\ \text{radians}}\]