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Rotating Bicycle Wheel

by kiwikahuna
Tags: bicycle, rotating, wheel
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Jun26-07, 11:51 PM
P: 61
1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. The attempt at a solution
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!
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Jun27-07, 06:18 AM
Astronuc's Avatar
P: 21,870
Perhaps this will help.

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.

see also
Jun27-07, 07:11 PM
P: 61
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.

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