A fan is rotating with a speed of 450 rec/minute. Afer being switched off it comes to rest in 10s. Assuming constant angular deceleration, calculate the number of recvolutions made by it before coming to rest.

Explanation

Here `f_(0)=450` rev/min. `= (450)/(60)` rev/s
`f_(0)=(15)/(2)` rev/s
`therefore` Initial angular velocity `omega_(0)=2pi f_(0)=15 pi` rad/s
At `t = 10 s, omega = 0`
`therefore` Angular acceleration `alpha = (omega - omega_(0))/(t)=(0-15 pi)/(10 s)=-(15)/(10)pi = -(3pi)/(2) rad//s^(2)`
`theta= omega_(0)t+(1)/(2)alpha t^(2)`
`=15pi xx 10-(1)/(2)((3pi)/(2))10^(2)`
`= 150 pi - 76 pi = 75 pi` rad
`therefore` No of revolutions `= (theta)/(2pi)=(75 pi)/(2pi)=37.5`