Need help figuring out precession rate

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    Precession Rate
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Discussion Overview

The discussion revolves around understanding the precession rate of a spinning bicycle wheel held by a person sitting in a chair. Participants explore the governing equations and factors that influence the rate of precession, including angular momentum and torque. The scope includes conceptual and mathematical reasoning related to rotational dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the factors that determine how fast they will spin when twisting a spinning bicycle wheel and seeks the appropriate equation for calculating the rotation.
  • Another participant suggests that the total angular momentum of the wheel and the applied torque are crucial for determining the precession rate, providing a formula ω = T/L, where T is torque and L is angular momentum.
  • A participant expresses intent to calculate angular momentum based on the provided guidance.
  • It is proposed that for a bicycle wheel, an estimate of the moment of inertia can be given by I=MR², where M is mass and R is radius.
  • One participant questions the inclusion of the radius in the precession rate equation, suggesting a simplified form w = T/(I*s) instead.
  • Another participant clarifies that the radius refers to the distance from the string to the wheel, implying that extending this radius would increase the precession rate, drawing a parallel to the length of their arms.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of the precession rate, particularly regarding the inclusion of the radius in the equations. There is no consensus on the final equation or the assumptions regarding the moment of inertia.

Contextual Notes

Participants note that the moment of inertia assumption (I=MR²) may not strictly apply as it assumes all mass is at a distance R from the center of rotation, which may not be accurate for the bicycle wheel.

Laguna2
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Hi.

I am working on a little project involving precession and I'm having a hard time figuring this one out.

I am sitting on a chair hold a spinning bycicle wheel in my arms. When I twist the wheel to the side I will start to spin.
What governs how fast I will spin? What is the equation to calculate the rotation? (Please also tell me if the results will be in Hz or rpm or whatever)

I'm currently studying physics but not at this level at all :p
I've been doing some research on my own and found an equation for when the wheel is hanging by a string, but it's not the same equation for what I am looking for is it?
 
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You need to know the total angular momentum of the wheel and the torque you are applying to the wheel's frame. Once you know that, the formula is going to be very simple.

ω = T/L

Where T is magnitude of torque, L is magnitude of angular momentum, and ω is the resulting angular frequency of precession. If you want it in Hz, you'll have to take ω/2π.
 
Thanks a lot! I will try to figure out angular momentum then :p
 
Usually you do that by measuring the precession rate...

Well, if you just need an estimate, for a bicycle wheel, an estimate I=MR² should be rather good.
 
So basically I could use the same equation as for the situation where the wheel is hangin by the string?

So I find for the precession rate:
w = (r * T)/(I * s) , where r is the length of my arms, T is the torque I apply, I is the moment of inertia of the wheel and s is the spin frequency of the wheel.
I would then spin around at a frequency w?
 
Where did the r come from? It should be just T/(I*s).

The I=MR² assumes that all of the wheel's mass is located distance R from center of rotation. That is not strictly speaking true, but it's kind of close.
 

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