What happens when you rotate a rigid body

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SUMMARY

This discussion centers on the dynamics of rigid body rotation, specifically the effects of attaching a fan to different points on a rod in free space. When a fan is attached to the center of mass of the rod, it induces a counterclockwise spin due to conservation of angular momentum. However, if the fan is attached to the end of the rod, the system experiences gyroscopic free precession, resulting in a wobble around the center of mass. The axis of rotation remains aligned with the center of mass, despite the wobbling motion.

PREREQUISITES
  • Understanding of rigid body dynamics
  • Familiarity with angular momentum and moment of inertia
  • Knowledge of gyroscopic effects and precession
  • Basic principles of conservation of momentum
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  • Research the principles of gyroscopic precession in detail
  • Explore the concept of moment of inertia as a tensor
  • Study the effects of non-symmetrical axes on rigid body rotation
  • Investigate practical applications of rigid body dynamics in engineering
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Physics students, mechanical engineers, and anyone interested in the principles of rotational dynamics and their applications in real-world scenarios.

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Hi,

I have a question about rigid body rotation. If I have a rod out in space in free float and I attach a battery powered fan to center of mass and then the fan is turned on to spin in a clockwise direction, then the rod should spin in a counterclockwise direction. This much I understand. But, what if, instead, the fan was attached to the end of the rod rather than to the center of mass? What would happen then?
Any help would be greatly appreciated!
 
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As a more general question, what would happen if you attached the fan to anywhere on the rod other than the center of mass? how would the rod and the fan spin together? Is what happens similar to a clothes washer that is unbalanced? Thanks in advance for any insight into this question!
 
If you are rotating about an axis that is not an axis of symmetry then the moment of inertia is a tensor meaning that the angular momentum does not line up with the axis of rotation. This gives you a wobble which is called gyroscopic free precession or torque-free precession.
 
Hi,

Thanks for your answer, would the system wobble around a certain point? Like, center of mass of the system?
 
Yes. There is no external force so the center of mass must remain at rest (assuming it started at rest). The axis of rotation will wobble, but will always pass through the center of mass.
 

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