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

Answer 1

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

Taking clockwise rotation as $-ve.$
Given,
Initial angular velocity,
${\omega }_1=-60\text{rad/sec}$
Final angular velocity,
${\omega }_2=-110\text{rad/sec}$, $t=2\text{sec}$
Angular acceleration $\alpha =\frac{{\omega }_2-{\omega }_1}{t}$
$\therefore \alpha =\frac{(-110)-(-60)}{2}$
$\Rightarrow \alpha =-25{\text{rad/sec}}^2$

So, angular acceration of fan blades is $25{\text{rad/sec}}^2$ in clockwise direction.