First slide

Angular velocity, Angular acceleration

Question

A fan makes 2400 rpm. If after it is switched off, it comes to rest in 10 s, then find the number of times
it will rotate before it comes to rest after it is switched off.

Moderate

A

400
B

100
C

200
D

50

Solution

Given, $f = 2400 rpm = \frac{2400}{60} = 40 Hz$
$∵ ω_{0} = 2 π f = 80 π q {rads}^{- 2}$
Now, $θ = [\frac{ω_{d} + ω}{2}] t$ +
$\Rightarrow θ = [\frac{80 π + 0}{2}] \times 10 = 400 π rad$
$∴$ Fan will turn angle 400 $π$ after it is switched off.
$\Rightarrow$ The number of rotation $= \frac{θ}{2 π} = \frac{400 π}{2 π} = 200$

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