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Note that this system has a single degree of freedom. Draw the free body
diagrams of the spool and block individually before writing down the NewtonEuler equations.
x
M
k G m
r R smooth no slip ME 563 – Fall 2011
Homework Prob. 1.2
Repeat Homework Problem 1.1 except here use the power equation. Compare
your result here with that found in Problem 1.1. ME 563 – Fall 2011
Homework Prob. 1.3
A thin homogeneous bar of mass m and length L is suspended by an inextensible
cord of length L/2. Let φ be the angular rotation of the cord and θ be the angular
rotation of bar, with both φ and θ measured positively counterclockwise from a
vertical line. A horizontal force f acts at the centroid G of the bar. A second force
F acts at end A of the bar in such a way that F always acts in a direction aligned
with the length of the bar. Note that this system has two degrees of freedom.
a) Determine the inertia coefficients for the system in terms of the generalized
coordinates φ and θ.
b) Determine the generalized forces due to the forces f and F acting on the
system in terms of the generalized coordinates φ and θ.
If it has been a while since you have dealt with rigid body kinematics, you might
want to see the review of rigid body kinematics in Appendix VI of the lecture
notes. L/2
B φ L
f θ
G A F...
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This document was uploaded on 12/23/2011.
 Fall '09

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