# Billiards rotational friction (side spin)

1. Jan 2, 2009

### REEPER

Hey all, not sure if this is the right place to post this, I apologise if it is not.

I've created a basic Billiards simulation but there's a type of friction I lack with regards to ball rotation.
Using an orthonormal basis to give an orientation: the surface of the Billiards table is aligned with the X-Z plane and the Y axis is perpendicular to the table's surface. My problem is that I don't know how to modelise friction for a ball's rotational velocity component around the Y axis.
I understand the ball will be sitting in a sort of cup in the felt and its friction in this cup will slow it down, but I'm not sure how best to represent this friction and what sort of coefficients I'm dealing with.
Any help with shedding some light on this would be greatly appreciated, thanks.

2. Jan 3, 2009

### Redbelly98

Staff Emeritus
Well, the friction produces a torque about the Y direction which will cause a spinning ball to stop rotating.

You may have to do an experiment: how long does it take a spinning ball to come to a stop, and then what coefficient will give the same spin-down time in the simulation?

The tricky part will be estimating the initial rotation rate of the ball.

3. Jan 3, 2009

### REEPER

I unfortunately don't have the equipment or the time to determine the deceleration rate along the Y axis in practice. I was hoping someone might know where I could find a frictional coefficient or deceleration rate for side spin between a billiards ball and the table felt, as I haven't had any luck thus far finding them myself.

edit:

I've found a link with a deceleration rate for ball-cloth spin, but I'm not certain if its for side spin

Last edited: Jan 3, 2009
4. Jan 4, 2009

### chaoseverlasting

I dont know if this is exactly right, but I think a constant torque independent of the angular velocity of the ball will cause it to stop. From the link you've found, the angular deceleration is given to be 11rads/s.

We know,

$$\tao =I\alpha$$
$$w=w_0 -\alpha t$$

For a solid sphere, $$I=\frac{2}{5}mr^2$$, using the second equation, equating $$\omega$$ to 0 (as the ball stops spinning) gives you the time required. The rest of the parameters are dependent on your simulation.

5. Nov 16, 2010

### velisch

hi there..

i hope someone is still reading this. i have got a tricky question and i am really not getting anywhere with my thoughts..

let's imagine someone is accelerating a pool ball up to certain angular velocity (picture --> ω) while the ball has no contact to the cloth.
then the ball is lowered onto the cloth.. due to the fricition it will move to the -x - direction. but how fast will it accelerate?
ball diameter: 2.25 in
ball mass: 6 oz
ball-cloth coefficient of sliding friction (m): 0.2
ball-cloth spin deceleration rate: 11 rad/sec2