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Question

When a ceilling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation):

A
18
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B
12
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C
36
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D
48
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Solution

The correct option is A 12
Let the initial angular velocity of the fan be w

Its angular velocity when the fan makes 36 rotation w1=0.5w

Using w22w21=2αS where S=2π(36) radian

(0.5w)2w2=2α×2π(36) 4πα=0.75w236

Let the fan makes n more rotation before coming to rest.

Using w23w22=2αS where S=2πn radian and w3=0

0(0.5w)2=2α(2πn)

OR 0.25w2=0.75w236×n n=12

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