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test123
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- Homework Statement
- Take a rope attached to the ceiling, with a rod perpendicular to it. On the end of the rod there is a spinning bicycle wheel that can be treated as a disk. What force causes the wheel to precess, if any?
- Relevant Equations
- T = r x F
L = I*w
dL/dt = T
In class, the prof. gave the following explanation for why the wheel precesses:
Whenever the wheel is spinning, it has a angular momentum perpendicular to its face. The torque due to gravity changes the direction of the angular momentum, causing precession.
However, this does not seem like a good enough explanation for this problem, because:
1. There is not an explanation as to why the angular momentum must be perpendicular to the wheel.
2. It does not explain where the force that causes precession comes from.
Below is my attempt to link her explanation to a force:
Diagram:
View attachment 371335
Explanation:
1. I draw my FBD. The dL represents the small change in L.
2. I combine dL and L to get L'. Experimentally, we know that the wheel will try to flatten itself at with the plane of rotation. In order for this to occur, a force, F must apply.
3. This is more evidence for the force. We know that the precession causes a z component of L. We don't start with any z component, and the torque due to gravity has no z component, so we must have some force in the x-y plane causing it.
Attempt at identifying force:
Based on my diagram I am 90% sure that there is a force, however I can not identify it. At first I thought the bearing of the wheel would give the force, but I don't know how it would know what direction the wheel is spinning. My next idea was that the wheel would become unstable when not rotating like it normally would, allowing external forces to push it in the direction of L'. Once the chaotic forces eventually pushed it toward L', it would stabilize. However, I don't like this solution either because it isn't very scientific sounding and would require some degree of luck.
Whenever the wheel is spinning, it has a angular momentum perpendicular to its face. The torque due to gravity changes the direction of the angular momentum, causing precession.
However, this does not seem like a good enough explanation for this problem, because:
1. There is not an explanation as to why the angular momentum must be perpendicular to the wheel.
2. It does not explain where the force that causes precession comes from.
Below is my attempt to link her explanation to a force:
Diagram:
View attachment 371335
Explanation:
1. I draw my FBD. The dL represents the small change in L.
2. I combine dL and L to get L'. Experimentally, we know that the wheel will try to flatten itself at with the plane of rotation. In order for this to occur, a force, F must apply.
3. This is more evidence for the force. We know that the precession causes a z component of L. We don't start with any z component, and the torque due to gravity has no z component, so we must have some force in the x-y plane causing it.
Attempt at identifying force:
Based on my diagram I am 90% sure that there is a force, however I can not identify it. At first I thought the bearing of the wheel would give the force, but I don't know how it would know what direction the wheel is spinning. My next idea was that the wheel would become unstable when not rotating like it normally would, allowing external forces to push it in the direction of L'. Once the chaotic forces eventually pushed it toward L', it would stabilize. However, I don't like this solution either because it isn't very scientific sounding and would require some degree of luck.