2011-03-13, 04:00 PM
This all is kind of weird to me, but it seems like what they're referring to with the top is two kinds of rotation.
First, the top is spinning about its axis, which is L.
![[Image: 4keC.png]](http://imm.io/media/4k/4keC.png)
Second, if L is not completely vertical (if the top is tilted, like in the diagram), then the force of gravity will apply a torque to the top that will cause it to tip over.
![[Image: 4keS.png]](http://imm.io/media/4k/4keS.png)
(T = r cross g goes into the page; the top rotates about O, clockwise on the page. Imagine the top isn't spinning, it'll just fall down.)
How those two interact with each other to cause the axis of L to move around, I don't really understand, but hopefully my interpretation of the situation helps.
Also for question 1, it says angular momentum calculated about a point on its path, which would imply that the bottom point of your triangle is actually on the line of motion (so your triangle is degenerate, and phi = 90).
First, the top is spinning about its axis, which is L.
Second, if L is not completely vertical (if the top is tilted, like in the diagram), then the force of gravity will apply a torque to the top that will cause it to tip over.
(T = r cross g goes into the page; the top rotates about O, clockwise on the page. Imagine the top isn't spinning, it'll just fall down.)
How those two interact with each other to cause the axis of L to move around, I don't really understand, but hopefully my interpretation of the situation helps.
Also for question 1, it says angular momentum calculated about a point on its path, which would imply that the bottom point of your triangle is actually on the line of motion (so your triangle is degenerate, and phi = 90).