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# Balls rolling with friction

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If a pool ball is moving and spinning across the table how does the sliding frictional force between the table and ball effects the velocity and angular velocity of the ball? I know frictional forces apply untill the rolling condition is met (w=vR where v is velocity, R is radius and w angular velocity) but does anyone know how the velocity and angular velocity cahnge to achieve this condition. I assume its something like: if wvr v'' = v + fgm(dt) w` = w - (5/fg(dt))/2RR where v is the inititial velocity, v'' the final velocity, f the sliding friction coefficient, g the gravitational acceleration, m the mass, dt the change in time, w the initial angular velocity, w'' the final angular velocity and R the radius. Does anyone know if this is right or can offer any improvements to the modell?

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Friction stuff is very complex (for me anyway). For static friction, the ball would start rolling if the tangencial force is greater than the vertical force (usually mass * gravity) times the coefficient of static friction.

|Ft| > u.|Fn|, the ball starts moving, else it doesn''t

|Ft| = sqrt(F.x*F.x + F.z*F.z);
|Fn| = |F.y|

for dynamic friction, I think it''s something like

Ff = -k.Vt

Vt being the tangencial velocity at the point of contact, k being a coefficient. And |Ff| is limited by another coefficient, a bit like static friction (I think it''s a similar coefficient).

so |Ff| <= u.|Fn|

When |Ff| becomes greater, limit it to u.|Fn|. The extra force can be considered as some extra energy dissipated, like generating a loud screeching sound for tires on the road, or heat.

That''s how I modelled the friction in a demo I made, and it gives satisfying results. However, I have to set k to a rather large value, like 200. That doesn''t seem right.

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