Question

A fan is rotating with angular velocity

100 rev s^{- 1}

. Then it is switched off. It takes

5 minutes

to stop.

(a)

Find the total number of revolutions made before it stops. (Assume uniform angular retardation)

(b)

Find the value of angular retardation.

(c)

Find the average angular velocity during this interval.

Accepted Answer

Use the equations of motion in the case of angular motion.

Given,

$ω_{0} = 100 rev s^{- 1}$ , $t = 5 \times 60 = 300 s$ and $ω = 0$ .

Now using the first equation of motion in the case of angular motion,

$ω = ω_{0} + α t$ .

So, the value of angular acceleration,

$\Rightarrow α = \frac{ω - ω_{0}}{t} = \frac{0 - 100}{300} = - \frac{1}{3} rev s^{- 2}$ .

Now using the second equation of motion,

$θ = ω_{0} t + \frac{1}{2} α t^{2}$

$\Rightarrow θ = 100 \times 300 - \frac{1}{2} \times \frac{1}{3} \times {(300)}^{2}$

$= 30000 - 15000 = 15000 rev$ .

Then the total angular velocity is defined as,

$ω_{av} = \frac{Total angle of rotation}{Total time taken}$

$= \frac{15000}{50 \times 60} = 50 rev s^{- 1}$ .

B M Sharma Solutions for Chapter: Circular Motion, Exercise 6: ILLUSTRATION 9.6

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Circular Motion, Exercise 6: ILLUSTRATION 9.6

Questions from B M Sharma Solutions for Chapter: Circular Motion, Exercise 6: ILLUSTRATION 9.6 with Hints & Solutions

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