Hello, I need help with calculating angular and CM (center of mass) velocity of a rolling ball. The ball is rolling on an inclined surface. What I have: - CM velocity (velocity of a ball itself) - Angular velocity ( w ) - Coefficient of friction ( coeff ) - Normal of a plane What I need to get: - New velocity of center of mass (ball itself) - New angular velocity I have already implemented collision detection and collision response (only calculating new velocity of a ball after collision, based on restitution). But I can't figure out how to make the ball roll properly on the surface. I want to take into account sliding of a ball (if tangent velocity + ball velocity is not equal to 0 then a ball slides on the surface) Thank you in advance.

I'm not an expert in such kind problem, so I can't give the formula. But I have done such analyses in university. This is a complicated problem. I could give you some hints.

I think you need to specify two more parameters, the mass and the moment of inertia of the ball. If the ball is put on the plane from still, then the ball will roll down without sliding with acceleration. But the evolution of the motion then is complicate.

But here is some strategy to solve:

1) Get the relationship between angular acceleration and the forces(gravitational force along the slope and friction);
2) Get the relationship between linear acceleration and the forces(gravitational force along the slope and friction);
3) Integrate the two accelerations to get two velocity;
4) Determine at what point the ball begins to slide, either because friction is less than frictional coeff. times normal force, or there is no matching of linear and angular velocities;
5) Repeat 1,2,3 for the sliding cases.

Then, you may fully describe the problem. Also, all you need from the normal vector is the slope of the plane in the direction the ball is falling, where you will find the concept of Directional Derivative useful.

P.S, good luck and hope it will not take a lot of your time to figure out. LOL

Not that this is a direct solution, but reading it in full may help you see how to solve your problem (it doesn't involve constant acceleration, but everything else):

http://archive.ncsa.illinois.edu/Classes/MATH198/townsend/math.html