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Originally Posted by theprgramerdude
When you said a torque tau is applied to the wheel, did you really mean the rod?
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No. Torque is applied to the wheel by the motor on the wheel. This torque on the wheel then tries to drive the wheel "forward", but it can't go straight "forward" because it is constrained by the rod to travel in a circle. But it can't travel along that circle until sufficient torque is applied to break the static friction with the floor.
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If you meant the wheel, then wouldn't that make the angle theta irrelevant to solving the problem?
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No. The angle of the wheel affects how much friction force the floor generates in response to the torque on the wheel.