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A fan is rotating at 90 rpm. It is then ...

A fan is rotating at 90 rpm. It is then switched OFF. It stops after 21 revolutions. Calculate the time taken by it to stop assuming that the frictional torque is constant.

Text Solution

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`n_(0)=90 rpm =1.5 rps therefore omega_(0) =2 pi n_(0)=3 pi (rad)/(s)`
The angle through which the blades of the fan move while stopping is `theta = 2 pi N = 2 pi (21) = 42 pi rad, omega = 0` (fan stops). Using equations analogous to kinematical equations of motion
`alpha (omega-omega_(0))/(t) =(omega^(2)-omega_(0)^(2))/(2 theta)`
`therefore (0-3 pi)/(t) =(0-(3pi)^(2))/(2(42pi)) therefore t=28 s`
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