Quote:
Originally Posted by Ether
Given the assumptions in the problem statement, the answer is 1 rad/sec.
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At steady-state, the net torque acting on the bot around its center of mass must be ZERO.
The only forces acting on the bot in the horizontal plane are the four friction forces (one at each wheel). The direction of these forces will start out aligned with the plane of each wheel, but will change as the robot begins to spin. Given the assumption about CoF being independent of speed and direction, the friction at each wheel will always point in the direction of the relative motion between the carpet and the wheel at the contact patch. This relative motion is the vector sum of the wheel tangential speed plus the carpet speed at the wheel due to the robot's motion.
When the robot spin reaches the point where the net torque around the center of rotation is zero, the spin will stop changing.
The robot weight (150 lbs) and CoF (0.8) were red herrings. Given the assumptions, their values do not affect the answer (as long as neither is zero).