A small wheel of radius a is constrained to roll along the interior wall of a large, horizontal ring of radius (R+ a): R

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A Small Wheel Of Radius A Is Constrained To Roll Along The Interior Wall Of A Large Horizontal Ring Of Radius R A R 1 (100.58 KiB) Viewed 16 times

A small wheel of radius a is constrained to roll along the interior wall of a large, horizontal ring of radius (R+ a): R ө a The angular position of the center-of-mass of the wheel with respect to the ring is and the rotation of the wheel is represented by 0. a) Write down the circumferences of the wheel and the ring. b) How many rotations does the wheel make around its center-of-mass while the center of the wheel completes one rotation around the center of the ring? c) Using the result from (b), write down an equation relating @ and (assuming the wheel rolls without slipping or sliding along the ring wall). d) The moment of inertial of the wheel around a vertical axis passing through its center-of-mass is lp, and the moment of inertia of the wheel around a vertical axis passing through the center of the ring is le. Find the Lagrangian of the wheel.