A cylinder of mass `5 kg` and radius `30 cm` and free to rotate about its axis receives an angular impulse of `3 kg m^(2) s^(-1)` initially, followed by a similar impulse after every `4` second. What is the angular speed of the cylinder `30 s` after the initial impulse ? The cylinder is at rest initially.

Explanation

Here, `m = 5 kg, r= 30 cm = 0.3 m`,
`omega_(0) = 0, omega = ?`
Angular impulse
= change in angular momentum
`3 = I (omega_(2) - omega_(1)) = (1)/(2)mr^(2) (omega - 0)`
`3 = (1)/(2) xx 5 (0.3)^(2) omega, omega = (40)/(3) rad//s`
From `omega = omega_(0) + alpha t`
`alpha = (omega - omega_(0))/(t) = (40//3 - 0)/(4) = (10)/(3) rad s^(-2)`
As angular impulse is imparted after every `4` second, i.e., at `t = 0, 4, 8, 12, 24 and 28 s`.
The last impulse continues upto `t = 32 s`
`omega omega_(0) + alpha t = 0 + (10)/(3) xx 32 = 106.7 rad//s`