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What if the W is not centered at L/2? Then, how can I calculate F?

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In fact the twist angle is assumed to be constant from the center of the cylinder out to its circumference. If we call the twist caused strain at any distance r from the center $ds, \ then\ \theta= \frac{ds}{r} \quad and \ ds=\theta*r$ Shear is $t=G*\epsilon= G*\theta*r \quad \text{or y in your equation}= G*yr$

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First, picture two disks, placed parallel, and close together. Draw a line through the center of each disk. Line up the lines. Are all the points on the lines the same distance apart? Now rotate one disk by a few degrees. Are all points on the lines the same distance apart? Have the lines drawn further apart at the center of the disks, or at the edges? ...

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