[BerntR]

I mentioned that one could mentally picture that there a million time-points that the orbiting object will pass through on its circular orbit around one circumference of the circle in one second.

Now, imagine that the orbiting object is at point A. Then, one millionth of a second later the object is at point C.

What forces are in play to move the orbiting object from point A to point C, and do those forces involve the use of energy?

Jeff,

You've already drawn two vectors in your figure, so let's just start by saying that a vector is a directed size. In our case it will either be a directed force or a directed velocity.

If the object is already moving in a circle you don't need the B force vector to move it from A to C. You only need a centripetal force from A to Origo to do that. So your diagram need an invard pointing vector to be complete. Origo is the center of the circle, btw.

The centripetal force simply adjust the direction a little all the time, so the object is forced to move in a circle instead of going straight ahead. It can be a string attached to a pole or it could be a physical path that forces the object to circulate. As long as there's no friction loss, air drag or other resistance that consumes energy, the object will spin forever.

The centripetal force doesn't do any work in a Newtonian sense. It doesn't increase the speed. It doesn't overcome any resistive loss if any of such is present. It only changes the direction of the mass movement.

If you apply a B force vector to the system the speed of the moving object will be increased. But only to the the extent that the force vector points in the same direction as the object is moving. It's the B forces that produces the swing speed.