# Skidding and rolling without slipping of a bowling ball

1. Nov 4, 2009

### chenying

1. The problem statement, all variables and given/known data

A bowler throws a bowling ball of radius R = 11 cm down the lane with initial speed v0 = 8.5 m/s. The ball is thrown in such a way that it skids for a certain distance before it starts to roll. It is not rotating at all when it first hits the lane, its motion being pure translation. The coefficient of kinetic friction between the ball and the lane is 0.22.

(a) For what length of time does the ball skid? (Hint: As the ball skids, its speed v decreases and its angular speed ω increases; skidding ceases when v = Rω.)

(b) How far down the lane does it skid?

(c) How fast is it moving when it starts to roll?

2. Relevant equations

v=r$$\omega$$

$$\omega$$f = $$\omega$$i - $$\alpha$$t

$$\tau$$ = I$$\alpha$$

3. The attempt at a solution

Ok......I really have no idea where to start. The clue they gave me gives me some ideas, but I still need some clarification. When the bowling ball starts to skid, does it have an initial angular speed? I know there is an initial and final velocity for the ball, but I'm confused about the angular speed of the ball.

2. Nov 5, 2009

### ehild

The motion of a ball consist of the translation of its centre of mass and rotation around the centre of mass. When it rolls, the displacement of the CM during one rotation is equal to the circumference, $s=r \omega$. (You can see it on a roll of paper), that is why $v=r \omega$ when the ball only rolls and do not skids.

When skidding, force of kinetic friction acts at the bottom where the ball touches the ground. This force decelerates the translational motion but its torque accelerates rotation.

Write the equation both for acceleration of CM and angular acceleration. At the beginning, the ball only skids, that is the angular velocity is 0. Determine how both the velocity of the CM and angular velocity of rotation depend on time. Find the time when $v=r \omega$ .

ehild