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I am trying to understand how the physics behind a curve ball in billiards work. Please see the attached picture:

curve ball

The red ball is meant to hit the blue ball. But to reach the blue ball, it has to go around the black one. I know to achieve such a curve, the cue must hit the ball left of the center. This will introduce a spin with the marked direction (clockwise). To me, this spin explains the first half of the curve (up to the black ball), but not how it is able to change its direction. What prevents the red ball from following the dashed orange path (which is much more intuitive to me)? The spin movement (clockwise direction) should move the ball away from its target.

I know (believe) this is related to the friction forces (kinetic friction, rolling friction) between the ball and the table and that there is also a force due to aerodynamic effects which can be neglected in this case. Has anyone a picture/description or can explain the acting forces?

Which forces act at which time to make the red ball follow the black curve?

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    $\begingroup$ Probably related physics.stackexchange.com/q/60681/25301 $\endgroup$
    – Kyle Kanos
    Dec 10, 2019 at 17:41
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    $\begingroup$ You have to strike the red ball on the top left side with the cue, and put both forward motion on it and a spin that is towards the left. If you start at the correct angle, the red ball will start moving to the right of the black ball and the spin on it will cause it to initially slip on the billiard table's felt, but it will "get a grip" in a few inches and start moving to the left. This action is known as "English" on the cue ball. See youtube.com/watch?v=vi3zZNwUcKg as a start. $\endgroup$ Dec 11, 2019 at 3:59

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The spin of the red ball has two components: the clockwise you mention, and the forward roll. Imagine the red ball is not moving forward but only spins clockwise, as you draw. You then roll it forward by a quarter revolution. Now it will role to the left. This is what gives the left curving.

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The force vector acting in the ball by the cue is a sum of a normal and a friction one. If there were no friction between cue and ball, that would follow a straight line to the right, without spinning.

The friction force is to the left. Its is certainly small for that material, so the composite force is to the right.

If the kick is just above the ball centre of mass, its axis of rotation is not vertical, but tilted to the right. So, the friction force from the table acts in the ball to the left all the way during its path.

The resultant trajectory is an arc as indicated by the black line.

The red line is typical for tennis or soccer balls, where the friction forces comes from the air, not from the floor.

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  • $\begingroup$ Sorry for my late response! I think I am starting to understand what's going on. But there is a thing that keeps me away from fully understanding: Imagine there is a tire instead of a ball. If one steers the tire in clockwise direction, the tire will roll to the right. I know, these are two different things, but isn't this similar to the first moment the balls spins and rolls? So, why does the ball tend to roll left and a tire rolls right, in the very first moment? It is quite hard for me to describe what I mean, therefore, I hope you understand :) $\endgroup$
    – user249315
    Dec 17, 2019 at 11:36
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The poster is correct that the ball would normally veer to the right with the left-side hit causing clockwise rotation. This is not a regular hit on ball on the left side of cue ball, however. This is a hit on the ball to get a curve in a Masse shot. To do that, one must hit the side of the cue ball but, also, one must raise the cue stick. This elevated cue stick causes the spinning cue ball to tilt to the left --- something it would not have done with a more-level cue stick (maybe 40 degree elevation hit required in the lesser curves). It is the tilt of the cue stick that results in the curve that is not present when using, in the example above, only left-side English on the cue ball with a level-to-the-cue-ball cue stick. This tilt to the left causes the clockwise rotation of the ball to veer left.

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