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

Step 1: The flywheel starts from rest, so the initial angular velocity is \(\omega_0 = 0\).

Step 2: The angular acceleration is \(\alpha = 0.5\ \text{rad/sec}^2\) and the time is \(t = 10\) seconds.

Step 3: The angular displacement under constant angular acceleration is given by \(\theta = \omega_0 t + \frac{1}{2}\alpha t^2\).

Step 4: Substituting the values, \(\theta = 0 \times 10 + \frac{1}{2} \times 0.5 \times 10^2 = 0.25 \times 100 = 25\) radians.

So the angular displacement after 10 seconds is 25 radians, matching option 2.