Does axles with constant angular velocity experience torque? Seen below is a dia

Question

Does axles with constant angular velocity experience torque? Seen below is a diagram of an axle with two frictionless bearings that hold the axle in place. If the wheels (and therefore axle) are turning with constant angular velocity does the axle experience any torque? What about shear stress?

Does axles with constant angular velocity experience torque? Seen below is a diagram of an axle with two frictionless bearings that hold the axle in place. If the wheels (and therefore axle) are turning with constant angular velocity does the axle experience any torque? What about shear stress?

Explanation / Answer

Though I believe to have this covered in your previous question, i'll still try to make you understand.........

As there is no differential movement of the wheels, there is no torsion produced, because there is no chance that there will be any rotation of one wheel with respect to the other wheel.

Consider a simple twisting of a rod. why do you think there is torsion at all? The answer is that one end has rotated and wants that other end also join it in rotation....when the other end is restrained from doing so, we say there is some torsion.

In the present case there is equal movement of wheels ....without any moment trying to restrain any movement so there is NO TORSION AT ALL.

About shear stresses..... In general shear stresses are produced by either torsion or bending. In the given case there is no torsion and hence no torsional shear stress, but there are forces being transferred to the axle through bearings in both horizontal and vertical directions which will lead to bending shear stresses.

Now comes the magnitude of shear stress....... If you assume that the axle is massless and all the weights are concentrated at wheels only, there won't be any bending shear stresses in between the two bearings as equillibrium demands that the force Fx1 be equal to the weight of one wheel (if on ground then equal to the reaction instead).

Thus there will be shear stresses present only in between the bearing and supports on their respective sides and these SHEAR STRESSES WILL BE THERE DUE TO BENDING only.

Please note that in the previous case the applied moment was restraining the rotation so there was torque but in the current problem the frictionless bearings don't offer any restraint so no torque at all.

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