An electric fan is revolving with a velocity of 210 rpm. When its motion is increased with the help of a regulator, it attains a velocity of 630 rpm in 11 s. What is the angular acceleration of the fan? Also calculate the number of revolutions completed by the fan in that 11 s ?

Explanation

Initial angular velocity,
`omega_(1) = (2pi xx 210)/(60) = 7pi " rad" cdot s^(-1)`
Final angular veloctiy, `omega_(2) = (2pi xx 630)/(60) = 21 pi " rad"cdot s^(-1)`
Now, from the equation `omega_(2) = omega_(1) + alpha` t we get, angular acceleration,
`alpha = (omega_(2) - omega_(1))/(t) = (21 pi - 7 pi)/( 11) = (14pi)/(11) = (14)/(11) xx (22)/(7)`
Again, angular displacement,
`theta = omega_(1) t + (1)/(2) alpha t^(2) = 7 pi xx 11 + (1)/(2) xx 4 xx (11)^(2)`
= 11 `(7 pi + 22)` = 484 rad
Since ina single revolution, the angular displacement is `2pi`, the number of revolutions
` = (theta)/(2pi) = (484)/(2pi)` = 77