[Jeff]

Yoda - in response to post #184.

My comment about a centripetal force moving outwards along the string was plain stupidity!!!

I believe that there is no centripetal force moving in either direction along the string. I believe that centripetal force is better defined as a force that causes an orbiting object to travel in a circular path rather than a straight line path.

Consider my orbiting ball example again.



Consider the orbiting ball at position X. If the hand (positioned at point A) abruptly stopped moving, then the hand would no longer pull on the string. What would happen to the ball in the absence of a pull force. It would veer off in a straight line direction at an tangent to the circumference of the circle (orbiting path). Now what would happen if the hand continued to move at its constant rate of speed from position A to position B. It would continue to exert a constant pull on the orbiting ball via the continuously taut string. The direction of the pull (transmitted via the taut string) is circular - from position X to position Y. The string is not directly pulling the orbiting ball to the center of the circle. That central pull to the center (a centripetal pull) is only a mental concept. One can see the orbiting ball being pulled from position X to position Y and we can mentally/conceptually divide the forces pulling the ball into two components - a force that pulls the ball forward in a straight line direction, and a force that causes centripetal acceleration (causes the ball to move along a circular path rather than a straight line path).

Note that the string is angled relative to the circumference of the orbiting ball's circle of rotation - where the axis of rotation is in the dead center of the circle.

You wrote-: " In your model, the ball is the orbiting mass and the hand is the axis of rotation. The hand is not the centripetal force (as you incorrectly state). It is, after all, the axis!"

Wrong! The axis of rotation is the dead center of the circle - both the hand's circle of rotation and the orbiting ball's circle of rotation. The hand is in orbit around the axis of rotation (dead center of the circle) like the ball - the only difference being that the radius of the hand's orbit is much smaller than the radius of the ball's orbit. As the hand moves in a circular fashion, it inherently is exhibiting a centripetal force that keeps it moving in a circular manner. The ball is moving at exactly the same rpm speed as the hand (due to it being pulled by a continuously taut string). In that sense, the hand's centripetal acceleration is transmitted to the ball by the taut string (which is inert) and the ball therefore also centripetally accelerates. In other words, if the hand centripetally accelerates (by the act of rotating in a circular manner), then the ball has to centripetally accelerate - because the connecting string is continuously taut and the taut straight string passively transmits the pull force from the hand to the ball.

Jeff.