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I composed a problem and initially thought it could be solved by purely analytical means, but it turns out it cannot.
The problem is as follows: a homogeneous ball of radius ##R## can rotate freely about its fixed center ##O##. Let ##J## denote its moment of inertia relative to an axis passing through the point ##O##. There is no gravity in this problem.
A beetle of mass ##m## sits on the ball. Initially, the system is at rest. Then, the beetle begins to crawl such that its trajectory draws a circle of radius ##b## on the ball. When the beetle returns to its initial position, it stops.
By what angle has the ball rotated when it reaches its final position?
I mean that a rigid body with a fixed point can be moved from any orientation to another by a single rotation. The question asks for the angle of this rotation between the initial and final positions of the ball once the beetle has stopped.
Interestingly, the answer does not depend on the beetle's law of motion along the circle and the ball stops as the beetle stops.
The problem is as follows: a homogeneous ball of radius ##R## can rotate freely about its fixed center ##O##. Let ##J## denote its moment of inertia relative to an axis passing through the point ##O##. There is no gravity in this problem.
A beetle of mass ##m## sits on the ball. Initially, the system is at rest. Then, the beetle begins to crawl such that its trajectory draws a circle of radius ##b## on the ball. When the beetle returns to its initial position, it stops.
By what angle has the ball rotated when it reaches its final position?
I mean that a rigid body with a fixed point can be moved from any orientation to another by a single rotation. The question asks for the angle of this rotation between the initial and final positions of the ball once the beetle has stopped.
Interestingly, the answer does not depend on the beetle's law of motion along the circle and the ball stops as the beetle stops.
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