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

• username2
In summary, the problem involves a uniform pool ball with mass 'm' and radius 'r' being given a horizontal impulse J at a distance br above its center, with a coefficient of kinetic friction between the ball and table of u. Assuming both the ball and table are rigid, the final speed can be expressed in terms of J, m, and B by considering the initial linear and angular speeds during the impulse, and then using the final speeds as the initial speeds for the second part where the ball is in a pure rolling state with negligible rolling friction.
username2
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
http://img507.imageshack.us/img507/4885/80038899xn3.png
I began the problem by using torque, but I doubt they want it in terms of an angle. Any pointers to approach this? thanks.

Last edited by a moderator:
username2 said:
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
http://img507.imageshack.us/img507/4885/80038899xn3.png
I began the problem by using torque, but I doubt they want it in terms of an angle. Any pointers to approach this? thanks.

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 by a moderator:
can someone solve this problem?

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