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.

 

[astrokreng]

Hello Bob,

The center of percussion is a point on an object where a force applied at that point will not produce any rotation. In the case of a billiard ball, this point is often referred to as the "sweet spot" and is typically located slightly off-center from the geometric center of the ball. When a cue stick strikes the ball at its center of percussion, the force is transmitted through the ball without causing any rotation. This means that the ball will continue to move in a straight line without any spin.

You are correct in your understanding that the force applied by the cue stick will have both horizontal and vertical components. The horizontal component will cause the ball to roll, while the vertical component will cause it to compress slightly on the table surface. However, this compression is very minimal and does not significantly affect the ball's trajectory.

In terms of thinking about the vertical component, it may be helpful to consider it as part of the overall force applied to the ball. The cue stick does indeed put an impulse into the ball, and this impulse can have both horizontal and vertical components. However, the vertical component is typically much smaller and does not play a significant role in the movement of the ball.

I hope this helps to clarify the concept of center of percussion and its effects on a billiard ball. Let me know if you have any further questions.