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First, are we assuming a no-slip condition between the wheels and the treadmill?

Second, is the treadmill itself at rest relative to ground, or is it somehow zooming a hundred miles an hour along the ground?

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Yes - no slip, as well as perfect bearings all around.

The treadmill mechanism itself it not moving relative to the ground, the conveyor part is. Just picture a moving walkway like in an airport, but much bigger (and faster).