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
nonelastic
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 workenergy
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 ModarresSadeghi, 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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 Fall '08
 MarkusBuehler
 Angular Momentum, Mass, Nicholas Makris, Sanjay Sarma

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