In article <email@example.com>, Peter <Poakfield@msn.com> writes: > Only a net force can produce an acceleration, and the acceleration > must be in the direction of the force. That is what Newton's second > law says.
Newton's second law applies in inertial frames. "tangential" isn't a single direction in a single inertial frame.
If you want to stick with a single rotating frame, Newton's laws can be made to work. But that involves Coriolis pseudo-force.
If you want to use a series of inertial tangent frames, you're not allowed to frame-jump without a coordinate system transformation. Choose the frames carefully. If you choose them so that the transformation does not contribute to tangential velocity then the "radial" force will have a "tangential" component. If you choose them so that the "radial" force has no tangential component then the transformations will convert radial velocity into tangential velocity. Your assertion fails either way.
If you want to use an inertial frame then "tangential" isn't a single direction your overly-simplistic application of Newton's second law is laughably invalid.