Billiard Ball Center Of Percussion Question, Please

[Robert11]

Hello,

This isn't my area, so please bear with me a bit.

Am curious about what happens when a cue stick strikes a billiard ball at the ball's center of percussion. I understand center of percussion concept, I think, and have looked at the math and equations, and O.K.

But, am not sure how to think about, or handle this:

Assume the cue stick is horiz, and strikes the ball at the cp.
The only was a "force" can be transmitted to the ball, I think, would be on a line perpendicular
to a plane tangent to the ball at the cp. True ?

Therefore, there would be a horiz and a vert force component acting on the ball.

It's the vertical component that bothers me.

The horiz one would be responsible for the "pure rolling" the ball would experience as it is being struck at the its cp. True ?

But what about this vertical component ?
Does it tend to push the ball into the surface ?

How should one think about this vertical component, assuming it does exist ?

Or should one consider the cue stick as just putting an "Impulse" into the ball ?
If so, does the Impulse have a vertical component also ?

Much thanks,
Bob

 

[Bob S]

If the cue strikes the ball at its vertical center of mass, the ball will want to slide at first, and gain angular velocity only via friction with the table. The ball has to be struck above its center of mass to impart both the linear momentum and angular momemtum. The moment of inertia of the ball is (2/5) mR². If it rolls w/o slipping, then R d(theta)/dt = v.