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nburo
8th May 2009 - 03:29 PM
Hello everyone, I'm trying find an interesting equation and maybe you can help me :

On a billiard table, I hit the cue ball with the cue stick with some angle so the ball starts rolling on the cloth, describing a curve. Let's say the friction force is 'f', the ball's radius is 'R' and the inertia tensor of the ball is 'I'. I'd like to find an equation for the angular velocity of the ball at time 't'. Notice that this isn't a 2D problem... we're in 3D and the ball has some spin in X-axis, Y-axis and Z-axis, so the equation : " w(t) = w(0) + a*t " doesn't work here.

So I'd like to find a general equation that tells me exactly the angular velocity of the ball at time 't'. Finally, I'll be able to integrate that equation so I get to know the angular displacement of the ball at time 't'.

Thanks for your help.
AlphaNumeric
9th May 2009 - 04:16 PM
It's either 1D or if you put spin on the ball which is not in the direction of it's initial velocity, it's 2d. And time.

If there's no spin it's a fairly well known homework problem and a decent book on classical mechanics will be covering it.
Trippy
10th May 2009 - 11:19 PM
QUOTE (AlphaNumeric+May 10 2009, 04:16 AM)
It's either 1D or if you put spin on the ball which is not in the direction of it's initial velocity, it's 2d. And time.

If there's no spin it's a fairly well known homework problem and a decent book on classical mechanics will be covering it.

Just me being curious here, but i'm guessing that this is because the only thing that affects the direction of the spin is the angle from verticle of the point where the pool cue strikes, and the distance from the center affects how much spin gets put on it, thus reducing what seems like a 3d problem to a 2d+1 problem?
nburo
11th May 2009 - 02:02 PM
so guys, any guess on an equation? I couldn't find anything in mechanic books, unfortunately.
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