A uniform disc of mass `m` and radius `R` I rotated about an axis passing through its centre and perpendicular to its plane with an angular velocity `omega_()`. It is placed on a rough horizontal plane with the axis of the disc keeping vertical. Coefficnet of friction between te disc and the surface is `mu`, find
(a). The time when disc stops rotating
(b). The angle rotated by the disc before stopping.

Explanation

`dtau=mu(dm)g.r`
`=mu((M)/(piR^(2)))(2pirdr)gt`
`thereforetau=int_(0)^(R)dtau=(2muMgR)/(3)`
Angular retardation `alpha=(tau)/(I)`
`=((2muMgR//3))/((1//2MR^(2)))=(4mug)/(3R)`
(a). `0=omega_(0)-alphat`
`thereforetau=(omega_(0))/(alpha)=(3omega_(0)R)/(8mug)`