Question

A fan initially rotating at $60\text{rad/sec}$ clockwise accelerates and aquires an angular velocity of $110\text{rad/sec}$ clockwise. If the angular acceleration of fan is constant and it takes $2\text{sec}$ to change its angular velocity, find the angular acceleration of the fan.

• A. $50{\text{rad/s}}^2$ in counterclockwise direction
• B. $25{\text{rad/s}}^2$ in counterclockwise direction
• C. $25{\text{rad/s}}^2$ in clockwise direction
• D. $50{\text{rad/s}}^2$ in clockwise direction

Answer 1

The correct option is C $25{\text{rad/s}}^2$ in clockwise direction

Taking clockwise rotation as $-ve$
Given,
Initial angular velocity,
${\omega }_i=-60\text{rad/s}$
Final angular velocity,
${\omega }_f=-110\text{rad/s}$,
and time taken $t=2\text{sec}$
Angular acceleration, $\alpha =\frac{{\omega }_f-{\omega }_i}{t}$
$\Rightarrow \alpha =\frac{(-110)-(-60)}{2}=-25{\text{rad/s}}^2$
So, angular acceleration of fan blade is $25{\text{rad/s}}^2$ in clockwise direction.