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Imagine two disks, A and B, each 1 foot in diameter. Each disk is permanently attached at its center to a vertical shaft which spins freely in any direction. Assume near-zero friction between the shaft and the bearings that hold it in place vertically. Below each disk, and also attached at their centers to the shafts, are two other smaller disks. Disk a is 6 inches in diameter. Disk b is 3 inches in diameter. Wrapped around the edges of the two smaller disks a and b is a belt, which cannot slip, forcing both sets of disks to rotate in a clockwise manner. Thus, when disk A completes one full rotation, disk B will have completed two full rotations. (At least I think that is what will happen.)

Imagine now two momentary/pulse forces of equal strength, emanating from the edges of larger disks A and B, and directed against each other at a 45 degree angle to a line that intersects the center of both vertical shafts. The effect of these two forces is that the disks will rotate away from each other at the point of the two forces, both in a clockwise direction. (Clockwise or counterclockwise doesn't matter to my question...just wanting us all to be on the same page.)

Question: Does the existence of the smaller disks connected by the belt either increase or decrease the effect of the forces upon each other? For example, is the force from disk A (with the larger of the two smaller disks) effectively increased over the force from disk B? If so, by how much? Or would the opposing forces need to emanate from the smaller disks here for there to be any mechanical advantage of force?

If we recompose the problem to be one where the opposing forces are still emanating from larger disks A and B, but disk A is 1 foot in diameter, disk B is 2 feet in diameter, and smaller disks a and b are both six inches in diameter and connected by the belt, which disk has the mechanical advantage, A or B?

ejn2017

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Joined: Sat Jun 17, 2017 5:40 pm

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