What is the Precession Frequency of a Rotating Bicycle Wheel?

[kiwikahuna]

Homework Statement

A professor holds a bicycle wheel rotating at 402 rev/min by a string attached to a weightless axle 20 cm from the wheel. The acceleration of gravity is 9.8 m/s^2. If all 7.5 kg of the wheel can be considered to be at its 53.6 cm radius, at what frequency in rpm does it precess?

Homework Equations

The Attempt at a Solution

Frequency=omega
I honestly am stumped with this problem but I was thinking of using a rotational kinematics equation to solve this.
The 402 rev/min can be converted to Omega initial. We can solved for Omega final using wf^2=wi^2 +2a(delta x).
Please help if you can!

 

[Astronuc]

Perhaps this will help.

http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html

If all 7.5 kg (the mass) of the wheel can be considered to be at its 53.6 cm radius, . . .

What is the moment of inertia I for a ring/hoop.
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#cmi

see also http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

 

[kiwikahuna]

Ok here's what I did.

(Mass of the wheel) * (Radius of the wheel)^2 (Omega given) - (Mass of the wheel)* (Length of the string)^2 * (Omega Unknown) = 0

(7.5 kg)(.536 m)^2(402 rev/min) - (7.5 kg) *(0.20 m)^2 * (Omega unknown) = 0

Is this the right to solve this problem? I feel as if I'm not getting/missing something.