# I can't seem to figure out how to start this

1. Mar 3, 2008

A Uniform pool ball mass 'm' and raidus 'r' begins at rest. It is given horizontal impulse J of fixed magnitude at a distance br above its center where -1<=B<=1. Coefficient of kinetic friction between ball and table is u. Assume both ball and table are rigid. Find an expression for the final speed in terms of J, m, and B

The only relevant equations I can think of are the moment of inertia of a solid sphere is 2/5MR^2 and J, the impulse, is the change in momentum, mass x velocity.

Here's an illustration

I began the problem by using torque, but I doubt they want it in terms of an angle. Any pointers to approach this? thanks.

2. Mar 3, 2008

### bjd40@hotmail.com

Try to do it this way; think of it in two parts. one during when the impulse J is given. it will acquire a linear speed and angular speed during that short period, both having initial value of zero. assume the final values. formulate equations involving rotational and linear motions ( of the form v= u +ft and the rotational counterpart of that).
now for the second part consider the final speeds(both rot and lin) of the first part as the initial speeds of the second part the final speed of the second part can be found considering the ball to be in a pure rolling state the linear speed v= wr, w being the final angular speed. consider rolling friction to be negligible. and kinetic friction(translational friction to be large enough to bring the ball to a pure rolling state from a rotational and translational motion after it released from the cue.

Last edited: Mar 4, 2008
3. Mar 6, 2008

### skt1BOXER

can someone solve this problem?