Need help figuring out precession rate

[Laguna2]

Main Question or Discussion Point

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?

 

[K^2]

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.

 

[Laguna2]

Thanks alot! I will try to figure out angular momentum then :p

 

[K^2]

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.

 

[Laguna2]

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?

 

[K^2]

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.

 

[Laguna2]

The r is the radius from the string to the wheel. If I extend the radius the precession rate will go up. It should be the same with my arms right? If I were able to extend them :)
http://en.wikipedia.org/wiki/Precession#Classical_.28Newtonian.29