What happens when you rotate a rigid body

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Discussion Overview

The discussion revolves around the dynamics of rigid body rotation, particularly focusing on the effects of attaching a fan to different points on a rod in free space. Participants explore how the position of the fan influences the rotation of the rod and the resulting motion, including concepts like wobbling and precession.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the outcome of attaching a fan to the end of a rod versus its center of mass, seeking to understand the resulting motion.
  • Another participant expands the inquiry to consider the effects of attaching the fan at various points along the rod, drawing a parallel to the behavior of an unbalanced clothes washer.
  • A participant introduces the concept of moment of inertia as a tensor when rotating about a non-symmetric axis, leading to a wobble known as gyroscopic free precession or torque-free precession.
  • In response, another participant confirms that the system would wobble around the center of mass, which remains at rest if no external forces act on it.
  • It is noted that while the axis of rotation wobbles, it will always pass through the center of mass of the system.

Areas of Agreement / Disagreement

Participants generally agree on the behavior of the center of mass remaining at rest and the wobbling motion of the axis of rotation, but the discussion includes varying perspectives on the implications of attaching the fan at different points on the rod.

Contextual Notes

The discussion does not resolve the specific outcomes of attaching the fan at various points, and assumptions regarding the system's initial conditions and external influences are not fully articulated.

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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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