Question

A wheel is at rest. Its angular velocity increases uniformly and become 80 radians second after 5 seconds. The total angular displacement is:

• A. 800 rad
• B. 400 rad
• C. 200 rad
• D. 100 rad

Answer 1

The correct option is C 200 rad

Initial angular speed, ${\omega }_0=0$ $rad/s$

Final angular speed, $\omega =80$ $rad/s$

Time taken, $t=5$ $s$

From kinematics:

$\omega -{\omega }_0=\alpha t$

$⟹80=\alpha \times 5$

$⟹\alpha =\frac{80}{5}=16$ $rad/s^2$

where, $\alpha$ is angular acceleration.

Also,

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

$⟹\theta =0+\frac{1}{2}\times 16\times 25$

$⟹\theta =200$ $rad$