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The motor of an engine is rotating about...

The motor of an engine is rotating about its axis with an angular velocity of 100 rev/minute. It comes to rest in 15 s, after being switched off. Assuming constant angular deceleration, calculate the number of revolutions made by it before coming to rest.

Text Solution

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The initila ngular velocity =100 rev/minute =(10pi/)rad/s`
FiN/Al angular velocity =0
Time interval =15s ltbr. Let angular acceleration be `alpha`. Using the equation `omega=omega_0+alphtat` we obtain alpha=(-2pi/9) rad/s^2`
The angle rotated by teh motor during this motion is
`theta=omega_0t+1/2alphat^2`
`=((10pi)/3 (rad)/s) (15s) -1/2 ((2pi)/9 (rad)/s)(15s)^2`
Hence the motor rotates thrugh 12.5 revolutions before coming to rest.
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