solid sphere of radius `r` is gently placed on a rough horizontal ground with an initial angular speed `omega_(0)` and no linear velocity. If the coefficient of friction is `mu`, find the time `t` when the slipping stops. in addition state the linear velocity `v` and angular velocity `omega` at the end of slipping

Explanation

m be the mass of the sphere.
Since, it is a case of backward slipping, force of friction is in forward direction. Limiting friciton will act in this case.
Net torque on the sphere about the bottommost point is zero. Therefore, angular momentum of the sphere will remain conserved about the bottommost point.
`L_(i) = L_(f)`
`:. I omega_(0) = I omega + m r v `
or `(2)/(5) mr^(2) omega_(0) = (2)/(5) mr^(2) omega + mr (omega r ) `
`:. omega = (2)/(7) omega_(0) and v = r omega = (2)/(7) r omega _(0)`