Question

question 17
a fan rotating with an initial angular velocity of 1000 rev/min is switched off. in 2.0 seconds, the angular velocity decreases to 200 rev/min. assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?
1200
20
10
100

Explanation:

Step1: Convert time to minutes

$t = 2.0\ \text{s} = \frac{2}{60}\ \text{min} = \frac{1}{30}\ \text{min}$

Step2: Use average angular velocity formula

Average $\omega = \frac{\omega_0 + \omega}{2} = \frac{1000 + 200}{2} = 600\ \text{rev/min}$

Step3: Calculate revolutions

$\theta = \text{Average}\ \omega \times t = 600 \times \frac{1}{30} = 20$

Answer:

20