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Question

A fan is rotating with angular velocity 100 revsec. Then it is switched off. It takes 5 minutes to stop. (i) Find the total number of revolution made before it stops. (Assume uniform angular retardation) (ii)) Find the value of angular retardation (iii) Find the average angular velocity during this interval.


A

No. of revolutions = 15000

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B

α = 23πrads2

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C

ωav = 100π rads

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D

ωav = 10π rads

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Solution

The correct option is C

ωav = 100π rads


ω0=ΔθΔt=100×2π=200π

t = 5 min = 5 x 60 = 300s

ω=ω0+αt

⇒ 0 = 100 x 2π + α (300)

α=200π300=2π3rad/s2...............................(ii)

θ=ω0t+12(23π)(3002)

= 60,000π π3× 90,000

= 60,000π – 30,000π

⇒ 30,000π radians

No. of revolution = θ2π=30000π2π = 15,000 rev ................................(i)

ωav=θt=30,000π300=100πrads......................(iii)


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