Collision of two billiard balls with spin

  • #26
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Oh Now I get it. During the interval of collision, the two balls lock gears, since they are rolling over each other without slipping. This makes the point of contact between the billiards the new pivot point.

So the normal force now wants to rotate the left ball clockwise arc about the new pivot point and the normal force on the right ball will want to rotate it in a counterclockwise arc about the new pivot point. But this shouldn't happen because gravity counters.

But, because they are rolling without slipping overeachother, both balls roll upwards at constant velocity( no net force vertical force allows this), while the pivot point remains fixed. So the normal force will be 0 briefly. But this is an extremely unstable equilibrium so both balls will rotate down, crashing into the table.

This causes a normal impulse that exceeds gravity.
 
  • #27
jbriggs444
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Oh Now I get it. During the interval of collision, the two balls lock gears, since they are rolling over each other without slipping. This makes the point of contact between the billiards the new pivot point.

So the normal force now wants to rotate the left ball clockwise arc about the new pivot point and the normal force on the right ball will want to rotate it in a counterclockwise arc about the new pivot point. But this shouldn't happen because gravity counters.

But, because they are rolling without slipping overeachother, both balls roll upwards at constant velocity( no net force vertical force allows this), while the pivot point remains fixed. So the normal force will be 0 briefly. But this is an extremely unstable equilibrium so both balls will rotate down, crashing into the table.

This causes a normal impulse that exceeds gravity.
Little of this makes much sense. Pivot points do not anchor the balls in place. Newton's second law still applies. No vertical acceleration = no change to normal force.

You seem to be taking the instantaneous reversal of rotation as a given and scrambling to find somewhere, anywhere where an impulsive torque could be found. You won't find one because there isn't one.
 
  • #28
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Little of this makes much sense. Pivot points do not anchor the balls in place. Newton's second law still applies. No vertical acceleration = no change to normal force.

You seem to be taking the instantaneous reversal of rotation as a given and scrambling to find somewhere, anywhere where an impulsive torque could be found. You won't find one because there isn't one.
If there isn't one, then how did the reversal of rotation happen? The reversal of velocity happened because of impulsive collision. So why not the reversal?
 
  • #29
jbriggs444
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If there isn't one, then how did the reversal of rotation happen? The reversal of velocity happened because of impulsive collision. So why not the reversal?
What makes you think that a reversal of rotation happened during the collision?

[Note that "because of" and "during" are different things]
 
  • #30
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What makes you think that a reversal of rotation happened during the collision?

[Note that "because of" and "during" are different things]

So the reversal happened during the collision but not because of it? So if the other ball wasn't there, the first ball would just keep moving forward but have its rotation changed?
 
  • #31
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So the reversal happened during the collision but not because of it? So if the other ball wasn't there, the first ball would just keep moving forward but have its rotation changed?
No. No reversal of rotation happened during the collision at all. You are trying to explain an effect that just does not happen.

Consider what happens after a collision in which a ball retains its rotational motion but reverses its linear motion.
 
  • #32
jbriggs444
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Going back and re-reading #17, the reversal of rotation is a given. We cannot argue with it. And I have been doing exactly that.

We know that the balls do not accelerate vertically so there can be no impulsive normal force. We are left with the possibility of an impulsive frictional force.
 
  • #33
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Going back and re-reading #17, the reversal of rotation is a given. We cannot argue with it. And I have been doing exactly that.

We know that the balls do not accelerate vertically so there can be no impulsive normal force. We are left with the possibility of an impulsive frictional force.
Thanks for confirming. Regardless, this discussion has really helped me clear up some critical misconceptions I held.

So basically, in a vacuum, when they collide, only linear velocity is reversed and each balls rotation stays the same.

On a table, it could be either way(reversal of rotation or not), depending on the type of material of the surface and material of the billiard balls. And we cannot tell ahead of time so it must be a given in the problem if we are to use frictional impulse.
 

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