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

Explanation

The intial angular velocity = 100 rev/minute ` = (10 pi//3) rad//s`
Final angular velocity `omega = 0 ` , Time interval t = 15 s .
Let the angular accelerations be `alpha` . Using the equation `omega = omega_(0) + alpha t ` , we obtain
` alpha = (-2pi//9) "rad/s"^(2)`
The angle rotated by the motor during this motion is `theta = omega_(0)t +1/2 alphat^(2)`
` = ((10pi)/3 (rad)/s)(15s) - 1/2 ((2pi)/9 (rad)/(s^(2)))(15s)^(2)`
` = 25 pi rad = 12.5 ` revolutions .
Hence the motor rotates through 12.5 revolutions before coming to rest .