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Week 5 - Moments of Inertia [4] [6]
Summary
What are the properties of the moment of inertia of a body? How do we relate
the moment of inertia about the center of mass to the inertia about another point?
Problem Set - 21 October 2005 Answers
Problem 1 - Schaum 7.3 
Show that the moment of interia of a body about any line Oa through the origin of coordinates is given by
IOa = (Ix x2
Iy y2
Iz z2
- 2 Ixy xy
- 2 Ixz xz
- 2 Iyz yz
) ( x2 + y2 + z2 )-1
where x,y,z are the coordinates of any point on Oa.
Problem 2 - Cone
Find the moments of inertia of a cone of height h, radius of
the base R, and mass M about the center of mass. What
are the moments of interia about the tip of the cone? What are they about the center of the base?
Problem 3 - Three Rods
Show that a system of three thin rods (of arbitrary length and mass)
is equimomental to any object.
Reading List
- ``Lagrangian Dynamics''
REF: Wells, D. A. 1967, Chapter 7.
- ``Classical Mechanics''
REF: Goldstein, H. 1980, Chapters 4-5.
- ``Mechanics''
REF: Landau, L. D., Lifshitz, E. M. 1988, Chapter 6.
Last modified: Wednesday, 30 November 2005 12:14:26
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