To speed up a flywheel from 60rpm to 120 rpm, energy equal to `9000 J` is requires. Calculate the moment of inertia of flywheel. Also calculate change in angular momentum of flywheel.

Explanation

Here,
`v_(1) = 60 "rpm" = 1` rpm
`v_(2) = 120 "rpm" = 2 rps, E = 9000 J`
`omega_(1) = 2pi v_(1) = 2pi xx 1 rad//s`
`omega_(2) = 2pi v_(2) = 2pi xx 2rad//s`
As `E = E_(2) - E_(1) = (1)/(2) I omega_(2)^(2) - (1)/(2) I omega_(1)^(2)`
`E = (1)/(2)I (16 pi^(2) - 4pi^(2)) = 6I xx pi^(2)`
`9000 = 6 I pi^(2), I = (9000)/(6pi^(2)) = 151.97 kg m^(2)`
Change in angular momentum
`DeltaL = I (omega_(2) - omega_(1))`
`= 151.97 (4pi - 2pi) = 151.97 xx 2pi`
`DeltaL = 954.98 kg m^(2) s^(-1)`