A solid ball of radius R is set spinning with angular speed omega about a horizontal axis. The ball is then lowered vertically with negligible speed until it just touches a horizontal surface and is released $($see figure$).$ If the coefficient of kinetic friction between the ball and the surface is mu$,$ find $($a$)$ the linear speed of the ball once it achieves pure rolling motion, $($b$)$ the distance it travels before it achieves this motion, and $($c$)$ the fraction of the ball's initial rotational kinetic energy that's been lost to friction.