(Solved): A uniform sphere of mass \( m \) and radius \( r \) is projected along a rough horizontal surface w ...

A uniform sphere of mass \( m \) and radius \( r \) is projected along a rough horizontal surface with a linear velocity \( v_{0} \). The coefficient of kinetic friction between the sphere and the surface is \( \mu_{k} \). Determine: \( (a) \) the time \( t_{1} \) at which the sphere will start rolling without sliding, and \( (b) \) the linear and angular velocities of the sphere at time \( t_{1} \).