Original Post
Hi everybody, Lately I've been trying to understand some of the forces acting on rotating cylinder shaped objects in order to better understand how wheels work. I've considered the following scenario and it's left me puzzled, because it does not seem to make sense. I know this sort of situation could never happen in the real world (because things are not perfect) but let me explain anyhow... Consider the following idealized situation: We have perfect cylinder travelling along a perfectly flat surface, lets say an infinite plane. The cylinder has a radius 'R', a linear velocity 'U' and an angular velocity 'W'. It makes contact with the ground at a point called 'C', which is directly underneath it's center of mass. Now consider for a moment that the only external force (or impulse in this case) acting on the Cylinder is friction (no aerodynamic drag forces). Lets say our simulation uses the following simple equation (per frame) to calculate a velocity loss for friction: F=KV Where F = Loss of velocity due to friction Where K = Coefficient of dynamic friction (i.e amount of friction) Where V = The velocity of the contact point 'C' on the sphere This is a velocity loss, but we could get to an impulse or force easily if we wanted to. Now the velocity of the contact point 'C' will be a combination of both linear and rotational velocity, and we will need to calculate this in order to calculate friction at that particular point. If a positive angular velocity means a clockwise rotation, and positive linear velocity means movement to the right, then to get the velocity of the contact point we would do the following: (note we are completly ignoring the Y/Z axis for this problem, 1 degree of freedom) V = U - R*W Where V = Velocity of contact point (for the x-axis) Where U = Linear velocity of object along x-axis Where R = Radius of the cylinder Where W = Angular velocity of the cylinder Simple enough? The velocity of the contact point is just a combination of rotational and linear velocity. Clockwise rotation will also produce a velocity in the opposite direction of the X axis at the contact point (because it is tangental to the rotating object). So consider if we plug in the following numbers: R = 10 (radius) W = 10 (angular velocity) U = 100 (linear velocity) If we calculate the velocity of the contact point using these numbers, we get a velocity of 0! V = 100 - (10*10) So in this case we get absolutely no friction, because the velocity of the contact point is said to be 0. Even if we calculated friction due to rotational and linear velocity separately, we would still end up with a net friction of 0- and torques would also balance. So in essence we have a situation where the two friction forces, due to rotation and linear movement cancel each other out- resulting in no friction. In a system with no other forces this would cause perpetual motion! Is this correct? Or am I missing something? It does not seem to make sense that an object could experience no friction even though it is moving and rotating at the same time. Here's a (crappy) diagram if that wasn't quite clear: 
