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Originally Posted by John
Would omega_w increase until the point on the motor curve where tau_k/r = mu_k * W * sin(theta)
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Yes.
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So the wheel would start spinning faster along its axis, but the rod would rotate at the same speed as before?
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It gets kind of messy. mu_k is not really constant in real life.
Typically, omega_p would increase as omega_w increases.
Under certain conditions, I think the system tries to minimize the relative speed between the floor and the wheel. I believe this occurs when omega_p = (r/L)*cosθ*omega_w