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2
5 mr 2
00
5 mr 2 0
00 5 mr 2
2
I
=
0
where m is the mass and r is the radius of the sphere.
The same sphere that is just a shell (i.e., has all its mass around the surface of the
sphere) has the following inertia tensor:
2
3 mr 2
00
3 mr 2 0
00 3 mr 2
2
I
=
0
A.3.3
C YLINDER
A cylinder, of uniform density, whose principal axis is along the Z axis, has an inertia
tensor of
12 mh 2
1
1
4 mr 2
+
0
0
1
1
I
=
12 mh 2
4 mr 2
0
+
0
1
2 mr 2
0
0
where m is the mass, r is the radius of the cylinder, and h is its height.
A.3.4
C ONE
A cone, of uniform density, whose principal axis is along the Z axis, has an inertia
tensor of
3
3
80 mh 2
20 mr 2
+
0
0
80 mh 2
3
20 mr 2
3
I
=
0
+
0
3
10 mr 2
0
0
where m is the mass, r is the radius of the cone, and h is its height. Unlike the other
shapes, the cone's center of mass isn't through its geometric center. Assuming the
center of the base of the cone is at the origin, the center of mass is at
0
0
1
4 h
where h is the height of the cone, as before.
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