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Originally Posted by Jared
This one is trickier...
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Yes it is. But this is all leading somewhere, and we're almost there.
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Im not sure if this is right, especially because the robot must now be constrained to rotate around its center, but I got 0.1748 rotations per second = 1.098 rad/sec.
Work:
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There was no link to your work.
Here's how you can check your answer:
1) at each wheel, use your answer to calculate the carpet velocity vector at that wheel due to robot rotation around the center of mass
2) at each wheel, combine (vector addition) the carpet velocity due to robot motion at that wheel (from step1) and the tangential velocity of that wheel to get the net carpet velocity at that wheel.
3) compute the normal force at each wheel, and use that to calculate the magnitude of the kinetic friction at each wheel.
4) at each wheel, use the net carpet velocity direction (from step2) at that wheel to split the kinetic friction magnitude at that wheel into X and Y components at that wheel
5) Sum the X components from step4. The sum should be zero at steady state.
6) Sum the Y components from step4. The sum should be zero at steady state.
7) Sum the torques around the center of mass due to the X and Y components from step4. The sum should be zero at steady state.
8) If any of the sums from steps 5, 6, or 7 are not zero, your answer is not correct.