hi hwang, i'm currently developing a pinball engine where the ball should move with respect to its rotation. I'm not that familar with mathematical notation, so I hope that you can explain some of the letters, you are using here. I'm trying to explain it for myself, so you may just correct me, if I'm wrong. These are beginner questions, but your execution fits perfectly to my current problem. Don't bother :) Fu=u mg: m,g is mass, gravity. Fu is the force, that acts to the ball, while he is rotating in a different speed than his linear velocity (friction). Is 'u' the velocity at the contact point (ball, table) ? Is 'u' a vector ? V= Vo - a*t: a is not more than just subtracting Fu with respect to time ? w = wo-t * (r u mg)/I: w is the angularVelocity, w0 is the old angularVelocity minus ( radius * u * mg ) / inertia with respect to time 't'. I wonder, if there are any if-conditions in your source or are the forces clearing for theirself ?