The "x" means cross product v=w x r This is the tangential velocity. So, a=(dw/dt) x r+w x (dr/dt) (dw/dt) x r is the tangential acceleration w x (dr/dt) is the radial (centripetal acceleration) I learned this from class. But where is the radial velocity? If we write s=T x r, then v=w x r+T x (dr/dt) Can T x (dr/dt) be interpreted as radial velocity? Now a=(dw/dt) x r + w x (dr/dt) + w x (dr/dt) + T x (d2r/dt2) =(dw/dt) x r + 2w x (dr/dt) + T x (d2r/dt2) Through a little geometry, I can show that dr/dt=w x r So, a=(dw/dt) x r + 2w x (w x r) + T x (d(w x r/dt) =(dw/dt) x r + 2w x (w x r) + T x ((dw/dt) x r + w x (w x r)) First question: have I violated physics and mathematics at once? Second question: can I simplify this? (I don't know the distributive/associative properties of "x") Third question: What do each of these terms signify? (ie, cent. accel, tang. accel, etc) Fourth question: What exactly is this vector T?