As a gyroscope precesses, its center off mass moves in a circle

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Discussion Overview

The discussion revolves around the behavior of a gyroscope and its center of mass during precession, particularly focusing on the forces acting on it, including normal force and torque. Participants explore the implications of a gyroscope's motion in both spinning and non-spinning scenarios, examining the conditions under which forces balance and how acceleration is affected.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant cites a textbook statement about the center of mass of a precessing gyroscope moving in a circle with zero vertical acceleration, questioning its applicability to a non-spinning flywheel scenario.
  • Another participant argues that in the case of a non-spinning flywheel, the vertical component of acceleration is not zero, as it would be falling, leading to a different relationship between normal force and weight.
  • A subsequent participant seeks clarification on what the normal force would equal in the case of a falling flywheel and what causes the pivot to exert a normal force when the flywheel is spinning.
  • Another response suggests that the normal force would be less than the weight of the flywheel, indicating that the flywheel's weight is a factor in the normal force exerted by the pivot.
  • One participant expresses confusion about the nature of the flywheel's motion, asserting that it is not simply falling but being rotated by torque.
  • Another participant counters that the center of mass of the flywheel is indeed accelerating downward, reinforcing the idea of vertical acceleration during precession.
  • A later contribution discusses the conditions under which a gyroscope's center of mass may oscillate vertically and the implications for the forces acting on it, suggesting that if the center of mass does not accelerate downwards at 1 g, an opposing force must be present.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of the flywheel and the conditions affecting the normal force and acceleration. No consensus is reached regarding the nature of the forces involved in both spinning and non-spinning scenarios.

Contextual Notes

Participants reference specific conditions and assumptions regarding the motion of the gyroscope and flywheel, including the effects of torque and the relationship between acceleration and normal force. The discussion highlights the complexity of these interactions without resolving the underlying questions.

aaaa202
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my textbook says:

"As a gyroscope precesses, its center off mass moves in a circle with radius r in a horizontal plane. Its vertical component of acceleration is zero so the upward normal force exerted by the pivot must equal mg."

Now wouldn't this always be true. I mean if u have a flywheel attached to a pivot and at first don't let it spin. Then the weight of it produces a torque that makes the arm rotate till it hits something, e.g. itself or the table it stands on. But its not translating linearly, so isn't there also a normal force exerted upwards by the pivot in this case? It just doesn't produce a torque since it's distance to the rotation axis is zero.
 
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aaaa202 said:
Now wouldn't this always be true.
No. In your example of the non-spinning flywheel, the vertical component of acceleration would not be zero. It's falling. There would be an upward normal force at the pivot, but it wouldn't equal mg.
 


what would it equal then? And what is it that makes the pivot exert a normal force in the case, where the flywheel IS spinning?
 


aaaa202 said:
what would it equal then?
Something less than mg. You could figure it out by computing the acceleration of the falling flywheel.
And what is it that makes the pivot exert a normal force in the case, where the flywheel IS spinning?
The flywheel has weight.
 


I don't get it. The flywheel isn't exactly falling it's just being rotated by the torque of its weight.
 


aaaa202 said:
I don't get it. The flywheel isn't exactly falling it's just being rotated by the torque of its weight.
Its center of mass is accelerating downward.
 


If the gyroscope is not precessing at the exact rate required to keep it near horizontal, it's center of mass is accelerating vertically. It could be oscillating up and down at it's rate of precession also oscillates.

If the gyroscope's center of mass isn't accelerating downwards at 1 g, then there's some force applied at the post opposing gravity. If the center of mass isn't accelerating vertically, then the upwards force from the post is m g.
 

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