A flywheel whose moment of inertia about its axis of rotation is `16kg-m^(2)` is rotating freely in its own plane about a smooth axis through its centre. Its angular velocity is `9rads^(-1)` when a torque is applied to bring it to rest in `t_(0)` seconds find `t_(0)` if
(a). The torque is constant and of magnitude 4`N-m`
(b). The magnitude of the torque after `t` second is given by `kt`.

Explanation

(a). Angular impulse
`=` change in angular momentum
`therefore taut_(0)=Iomega`
`theret_(0)=(Iomega)/(tau)=(16xx9)/(5)=36s`
(b). `int_(0)^(t_(0))taudt=Iomega`
`thereforeint_(0)^(t_(0))kdt=Iomega`
`therefore(kt_(0)^(2))/(2)=Iomega`
`thereforet_(0)=sqrt(Iomega)sqrt((2)/(k))`
`=sqrt(16xx9)sqrt((2)/(k))=12sqrt((2)/(k))`