A billiard ball is at rest on a billiard table. The player hits the ball with the stick at an height h above the center of the ball, so Vcm just after the hit is v0. The final Vcm of the ball is 9/7 * v0. Prove that h=4/5 * R I have here a question and as you can see Vcm at the final stage is higher than Vcm at the initial stage. This is a bit bizzard because intuativley you'd expect that the kinetic friction will act at the opposite direction of movement and slow the ball down. But I think that here, from the moment just after the ball is hit and moves in v0, and until the final stage where it's moving in 9/7 * v0 (Which I suspect is rolling without slipping mode) - the kinetic friction acts to the left - and so it generates linear acceleration to the left (as it's the only force acting to the left after the hit from the stick) which is accountable for the increase in Vcm, and at the same time it generates clock-wise angular accelration which decreases w (via the torque from the kinetic friction). So in the initial stage wR>Vcm and this friction force to the left makes it possible for the system to achieve Rw'=V'cm and to maintain rolling without slipping mode. Am I right? Is it the same situation when you're in a standing car and you push the gas all the way down? the tires spin very fast but the car isn't moving almost at all... until it finally does.