Terry Blanton wrote:
Here's a quick picture showing some of the most important forces (nb -- those black force arrows on the ramp have somewhat arbitrary directions):From: "Stephen A. Lawrence" <[EMAIL PROTECTED]>
If you don't understand this then you need to brush up on your physics.
Let's talk about the physics. A magnetic gradient pulls the ball up a ramp. Suddenly there's a hole in the ramp and gravity pulls the ball through the hole. The ball is still spinning when it falls. What imparted the angular momentum?
http://physicsinsights.net/images/ball-rolling-up-ramp.png
From the point of view of the ball, as it accelerated up the ramp, the ramp itself applied a tangential force to the surface of the ball which caused it to spin; thence came the angular momentum (in the frame of reference of the ball).
Angular momentum must be measured at a particular point in space. It only makes sense to talk about it with regard to a particular origin. In particular, it's conserved, but that statement only makes sense in a situation where you've chosen one point about which to measure the total value of L. So let's say we measure it at the point the ball lands on when it hits the ground after falling through the hole. From that POV, as the ball moves up the ramp, the ball gains angular momentum both because of its spin and because of the motion of its center of mass along a line which doesn't pass through the point we have (arbitrarily) chosen as the center of our coordinate system. At the same time, the RAMP gains angular momentum which is equal and opposite to the angular momentum of the spin of the ball, as a result of the force the BALL exerts on the ramp as it spins up. Finally, the MAGNET gains angular momentum which is equal and opposite to the angular momentum due to the motion of the ball's center of mass along a line which doesn't pass through the origin.
Now, the ramp is not accelerating in these coordinates, despite the force the ball exerts on it. So, the ramp is also being acted on by other forces (it's attached to the apparatus which is attached to the floor which is attached to the ground) and the L gained by the ramp is actually passed to the environment. Similarly, the magnet doesn't accelerate; its L value is also passed to the environment. But what is "the environment"? It's the Earth itself, which is so massive that we don't normally notice tiny changes in its angular momentum due to things like balls rolling up ramps. In other words, the Earth itself provides an essentially infinite source/sink for L, which is one reason why it's not always apparent that L is really conserved in real-world situations.
