Hello:
I'm working on a difficult problem. Imagine a wheel, dangling from an axle, allowed to spin freely. If you tape a weight to the rim of the wheel, then that section of the rim will rotate to the bottom, right? Now ... Imagine the axle is not perfectly in the middle of the wheel. That "Offset" (or runout) will cause the wheel to rotate, even if the wheel is perfectly balanced around it's true center point. My question is this: How much offset (runout) will be equal to adding 3 grams of weight to the wheel, 0.216 meters from the exact center of the wheel.
Weight of wheel: 19000g (19 kg).
Diameter of wheel: 0.725 meters
Assumptions: No friction from axle. Wheel is uniformly dense across it's structure (the wheel is uniformly constructed with wheel weight evenly distributed).
Calculating the rotational force of the added weight is very simple: 3g x 0.216m = 0.648 meter-grams of torsion.
Calculating the rotational force caused by the axle offset is much more difficult, since it's a round wheel, not a simple horizontal bar. I'm sure there will be integrals involved in this, but I just can't seem to set up the problem for it. Any help you could provide would be much appreciated.