A fly wheel rotates with a uniform angular acceleration. If its angular velocity increases form `20 pi` rad/s to `40 pi` rad/s in 10 seconds. Find the number of rotations in that period.

Explanation

Initial Angular Velocity `omega_(0) = 20 pi" "rad s^(-1)`
Final Angular velocity `omega = 40 pi" "rad s^(-1)`
time taken, t = 10 s
No. of rotations/s = ?
`omega = omega_(0) + alpha t`
`alpha = (omega-omega_(o))/(t) = (40 pi - 20 pi)/(10) = (20 pi)/(10) = 2pi`
`alpha = 2 rads^(-1)`
`theta = omega_(o)t + (1)/(2) alpha t^(2)`
`= 20 pi xx 10 + (1)/(2) xx 2pi xx 10 xx 10`
`= 200 pi + 100 pi`
`theta = 300 pi`
No. of rotations/sec. `= (theta)/(2pi) = (300pi)/(2pi)`
= 150 rotations.