Question

When a ceiling fan is switched on it starts from rest, while completing the ${10}^{th}$ revolution it has angular velocity of $40\text{rad/s}$ , find the angular acceleration of the fan ? (Assume uniform angular acceleration)

• A. $\frac{40}{\pi }{\text{rad/s}}^2$
• B. $\frac{50}{\pi }{\text{rad/s}}^2$
• C. $\frac{20}{\pi }{\text{rad/s}}^2$
• D. $\frac{25}{\pi }{\text{rad/s}}^2$

Answer 1

The correct option is A $\frac{40}{\pi }{\text{rad/s}}^2$

We know that, by the equation of motion under constant acceleration,

${\omega }^2={\omega }_0^2+2\alpha \theta$,
$\theta =2\pi n=2\pi \left(10\right)=20\pi$ where $n$ is the number of rotation and is given that it starts from rest, so ${\omega }_0=0$

we get,
${\omega }^2=2\alpha \times \theta =2\alpha \times 20\pi$
after $5$ revolution it is given that angular velocity becomes $(\omega =40\text{rad/s})$

$\Rightarrow {40}^2=40\pi \times \alpha$, $\alpha =\frac{40}{\pi }{\text{rad/s}}^2$

Option A is the correct answer.