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Endemoniada

Adding Spin ?

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Endemoniada    430
Hi guys, I want to add some spin to my moving pool balls (not really pool balls but close enough.) I''m mostly concerned with how the ball will reflect off a surface if it has spin on it. So for example, if the ball is heading directly towards a wall (heading opposite the wall''s normal) and is spinning clockwise which way will it go after it hits ? How do I calculate that ? Any help is appreciated.

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Timkin    864
If the surfaces of collision are frictionless, then there will be no effect from spin in the rebound trajectory. However, in realistic situations, there exists a frictional force generated by the ball on the cushion, in the direction of rotation (which is parallel to the plane face of the cushion), which generates a reactionary force by the cushion, onto the ball.

The magnitude of this reactionary force depends on the Impulse applied by the ball (the force times the collision duration).
This force is proportional to the speed of rotation (angular velocity) of the ball and the collision duration is proportional to the speed of the ball relative to the normal of the collision plane. The cushion then applies a reactionary force in the opposite direction. The magnitude is equal if energy is conserved in the collision. You''d probably want to only apply a percentage of the reactionary force... and perhaps add a very small random perturbation to this value.

So, in terms of your example, the ball would have a positive velocity component in the opposite direction of the rotation, measured at the point of collision. If the ball were rotating clockwise (looking down from above) then it would have a velocity component to the left, when facing the cushion.

Also remember that if you are simulating an elastic collision, the total momentum should be conserved, which means linear and angular momentum. Typically some of the angular moment will be transferred into linear momentum parallel to the collision plane to generate that velocity component.

If you wanted to get very technical with your spin simulation, then you would also need to simulate the small but measurable force generated perpendicular to the direction of motion of the ball, by the imbalance of frictional forces in the contact pad between the ball and the table felt. It''s because the ball doesn''t have a point contact that you can use spin to curve the trajectory of the ball along the table.

If you want the equations for all of these concepts, most first year undergraduate physics texts will contain them.

Cheers and good luck,

Timkin

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