# A ceiling fan is rotating with an angular velocity of 10 rad/s. It takes 40 s to stop when it is switched off. The average angular velocity during this interval is (assume uniform angular retardation): A 5 rad/s B 4 rad/s C 2 rad/s D -5 rad/s

## Question

A ceiling fan is rotating with an angular velocity of $10 \mathrm{rad} / \mathrm{s}$. It takes 40 s to stop when it is switched off. The average angular velocity during this interval is (assume uniform angular retardation):

A $5 \mathrm{rad} / \mathrm{s}$

B $4 \mathrm{rad} / \mathrm{s}$

C $2 \mathrm{rad} / \mathrm{s}$

D $-5 \mathrm{rad} / \mathrm{s}$

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## Answer

**:**

The correct option is **A**: $5 \ \mathrm{rad} / \mathrm{s}$.

Given:

- Initial angular velocity, $ \omega_0 = 10 \ \mathrm{rad} / \mathrm{s} $
- Final angular velocity, $ \omega = 0 $

Assuming **uniform angular retardation**, the **average angular velocity** can be calculated using the formula:
$$
\omega_{\text{avg}} = \frac{\omega_0 + \omega}{2}
$$

Substituting the given values: $$ \omega_{\text{avg}} = \frac{10 \ \mathrm{rad/s} + 0 \ \mathrm{rad/s}}{2} = 5 \ \mathrm{rad/s} $$

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