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Question

The motor of an engine is rotating its axis with an angular velocity of 100 rev per min. It comes to rest in 15 s after being switched off, assuming constant angular deceleration. What is the number of revolutions made by it before coming to rest ?

A
12.5
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B
40
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C
32.6
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D
15.6
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Solution

The correct option is A 12.5
Given:

The angular velocity of motor,

ωi=100 rev/min=100 RPM

ωi=100×2π60=10π3 rad/s

Motor comes to rest in 15 sec, applying kinetic equation:

ωf=ωi+αΔt

putting the value

0=10π3+α(15)

α=10π45 rad/s2

Again applying kinetic equation,

ω2f=ω2i+2αΔθ

0=(10π3)2+2(10π45)Δθ

20π45Δθ=100π29

Δθ=25π rad

Total number of revolutions made before coming to rest is,

n=Δθ2π

n=25π2π=12.5

Hence, option (a) is correct.

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