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# ps5 - 2.003J/1.053J Dynamics and Control I Fall 2007...

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2.003J/1.053J Dynamics and Control I Fall 2007 Problem Set 5 Out: Wednesday, 10 October, 2007 Due: Monday, 15 October, 2007 1. Pulley problem Recall the pulley problem we solved so far again and again. A pulley of radius R is rigidly fixed to the wall as shown in the figure. A point mass is attached to one end of a non-elastic string of length l o and the other end of the string is fixed to the top of the pulley as shown in the figure. Initially the mass is held such that the string is tight and horizontal and is suddenly released. Note that gravity acts. In one of the problem sets we found the equation of motion of the mass using Newton’s laws and the work-energy principle. Now find the equation of motion of the mass using the equation that relates the torque and the angular momentum about an arbitrary point (the one with the “pesky term”). g l o Cite as: Sanjay Sarma, Nicholas Makris, Yahya Modarres-Sadeghi, and Peter So, course materials for 2.003J/1.053J Dynamics and Control I, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.

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ps5 - 2.003J/1.053J Dynamics and Control I Fall 2007...

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