The moment of inertia of a body about a given axis is `1.2 kg m^(2)`. Initially, the body is at rest. In order to produce a rotational `KE` of `1500 J`, for how much duration, an acceleration of `25 rad s^(-2)` must be applied about that axis ?

Explanation

Here, `I = 1.2 kg m^(2), omega = 0`,
`E_(1) = (1)/(2)I omega_(0)^(2) = 0`
`E_(2) = (1)/(2) I omega^(2), E = 1500 J, t = ? alpha = 25 rad//s^(2)`
As `E = E_(2) - E_(1) = (1)/(2)I omega^(2) - 0 = 1500`
`:. omega = sqrt((2xx1500)/(I)) = sqrt((3000)/(1.2)) = sqrt(2500)`
`= 50 rad//s`
From `omega = omega_(0) + alpha t`
`t = (omega - omega_(0))/(alpha) = (50 - 0)/(25) = 2 s`