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The tension on the rod is not the only force acting on the wheel+motor assembly, so you can't set it equal to (WL/g)(omega_p)^2
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I said that centripetal force = tension minus friction parallel to the rod. Is there another force in addition to those two?
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Angular acceleration is zero.
Tangential acceleration is the rate at which the tangential velocity is changing. Since the tangential velocity is not constant, the tangential acceleration is not zero.
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I'm a little confused by this statement. Let me see if my understanding of circular motion is right, or if my physics teachers have been teaching me falsehoods. An object moving in a circle is always accelerating. That acceleration has two components, one that is tangential and one that is centripetal. The centripetal component is (mv^2)/r and the tangential component is the derivative of ds/dt, where s is the arc length. ds/dt is equal to d(theta)/dt times radius and tangential acceleration equals angular acceleration times radius.
In this problem the radius is constant and d(theta)/dt is constant as well. That means that angular acceleration is zero and tangential acceleration is also equal to zero.
(Maybe the problem is my axes. I created another system where one axis is always perpendicular to the rod and the other is always perpendicular. Then the centripetal acceleration is actually constant in both direction and magnitude, and I think tangential velocity is also actually constant)