Originally Posted by waspy77
As the velocity is increased, then a force is generated tangentially in the direction of the velocity.
As the velocity is decreased, then a force is generated tangentially in the direction opposite to the velocity.
If the acceleration is proportional to the angular position, then you end up with a variation of Harmonic Motion.
Draw tangential force lines around a circle maximum length at the bottom reducing poportionally as you approach the top, reversing directions and increasing back to the bottom. You will now see that summed around the circle there is a net force. With two running counter to each other, you will see that all lateral forces are cancelled out.
If you can disprove this mathematically then please do.
Waspy, i'm sorry to have to say that this really is just garbage. If you also considered the centrifugal force radial to the circle you would see that everything goes to producing no net momentum change over a cycle. Better still use lateral symmetry to project the system to 1D and you can see directly that reversing the direction at each end cancels any acceleration.
I don't have time to discuss the symantics of force impulse vs momentum (we engineers usually use whatever gives the quickest answer), but can just see this thread getting hung up on details.