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Question

When a ceiling fan is switched on it starts from rest, while completing the 10th revolution it has angular velocity of 40 rad/s , find the angular acceleration of the fan ? (Assume uniform angular acceleration)

A
40π rad/s2
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B
50π rad/s2
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C
20π rad/s2
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D
25π rad/s2
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Solution

The correct option is A 40π rad/s2
We know that, by the equation of motion under constant acceleration,

ω2=ω20+2αθ,
θ=2πn=2π(10)=20π where n is the number of rotation and is given that it starts from rest, so ω0=0

we get,
ω2=2α×θ=2α×20π
after 5 revolution it is given that angular velocity becomes (ω=40 rad/s)

402=40π×α, α=40π rad/s2

Option A is the correct answer.

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