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Unformatted text preview: 2.003J/1.053J Dynamics and Control I Fall 2007 Problem Set 6 Out: Monday, 15 October, 2007 Due: Monday, 22 October, 2007 1. A disc sliding in a circular well A circular disc of radius r and mass m is sliding in a semi-circular well of radius R as shown in the figure below. The contact between the disc and the well is frictionless . Let O be the center of the semi-circular well. Let C represent the center of the disc and let Q be some fixed point on the edge of the disc. At t = 0, the disc is held such that Q is at the tip of the well as shown in the figure. The disc is then released. Note that gravity acts. a. Where is the instantaneous center of rotation for the disc, if it exists? b. Find the equation of motion of the disc. c. Find the equation of motion of the disc using the work-energy principle (Take the derivative to verify whether the answer matches with the answers in the above part). O C m,r g C Q Cite as: Sanjay Sarma, Nicholas Makris, Yahya Modarres-Sadeghi, and Peter So, course materials for 2.003J/1.053JCite as: Sanjay Sarma, Nicholas Makris, Yahya Modarres-Sadeghi, and Peter So, course materials for 2....
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