Abstract
The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.
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References
1.
Halliday
D.
Resnick
R.
, Physics , 3rd edn , John Wiley , New York , 1978 .
2.
Sears
F. W.
Zemansky
M. W.
Young
H. D.
, University Physics , 7th edn , Addison-Wesley , Reading, MA , 1987 .
3.
French
A. P.
, Newtonian Mechanics , Norton , New York , 1971 .
4.
Skinner
R.
, Mechanics , Blaisdell , Waltham, MA , 1969 .
5.
Serway
R. A.
, Physics for Scientists and Engineers/with Modern Physics , Saunders , New York , 1983 .
6.
Becker
R. A.
, Introduction to Theoretical Mechanics , McGraw-Hill , New York , 1954 .
7.
Symon
K. R.
, Mechanics , 3rd edn , Addison-Wesley , Reading, MA , 1971 .
8.
Fowles
G. R.
, Analytic Mechanics , Holt, Rinehart & Winston , New York , 1962 .
9.
Desloge
E. A.
, Classical Mechanics , Vol. 1 , John Wiley , New York , 1982 .
10.
Spiegel
M. R.
, Theoretical Mechanics , McGraw-Hill , New York , 1967 .
11.
Goldstein
H.
, Classical Mechanics , 2nd edn , Addison-Wesley , Reading, MA , 1980 .
12.
Corben
H. C.
Stehle
P.
, Classical Mechanics , 2nd edn , John Wiley , New York , 1960 .
13.
Landau
L. D.
Lifshitz
E. M.
, Mechanics , 3rd edn , Pergamon , Elmsford , 1976 .
14.
Desloge
E. A.
, Classical Mechanics , Vol. 2 , John Wiley , New York , 1982 .
15.
Halfman
R. L.
, Dynamics , Vol. 1 , Addison-Wesley , Reading, MA , 1962 .
16.
Housner
G. W.
Hudson
D. E.
, Applied Mechanics—Dynamics , 2nd edn , Van Nostrand , New York , 1959 .
17.
Beer
F. P.
Johnson
E. R.
Jr.
, Vector Mechanics for Engineers , 4th edn , McGraw-Hill , New York , 1984 .
18.
Den Hartog
J. P.
, Mechanics , Dover , New York , 1961 .
19.
Routh
E. J.
, Dynamics of a System of Rigid Bodies (Elementary Part) , 7th edn , Dover , New York , 1960 .
20.
Thomson
W.
Tait
P. G.
, Principles of Mechanics and Dynamics , Part 1, Dover , New York , 1962 .
21.
Jeans
J. H.
, An Elementary Treatise on Theoretical Mechanics , Dover , New York , 1967 .
22.
MacMillan
W. D.
, Dynamics of Rigid Bodies , Dover , New York , 1960 .
23.
Whittaker
E. T.
, Analytical Dynamics of Particles and Rigid Bodies , 4th edn , Cambridge University Press , London , 1965 .
24.
Beyer
W. H.
, (ed.), CRC Standard Mathematical Tables , 28th edn , CRC Press , Boca Raton, FL , 1981 .