4. Obtain the moment of inertia tensor of a thin uniform ring of radius R, and mass M, with the origin of the coordinate system placed at the center of the ring, and the ring lying in the xy plane. Linear mass density: R de λ = Differential mass: de R 8 Hint: x= R cose; y = R sine X dm M 2TR =- XRd0 = de
4. Obtain the moment of inertia tensor of a thin uniform ring of radius R, and mass M, with the origin of the coordinate system placed at the center of the ring, and the ring lying in the xy plane. Linear mass density: R de λ = Differential mass: de R 8 Hint: x= R cose; y = R sine X dm M 2TR =- XRd0 = de
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Mathematical Physics 2
Topic: Tensor Analysis
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Transcribed Image Text:4. Obtain the moment of inertia tensor of a thin uniform ring of radius R, and mass M, with the
origin of the coordinate system placed at the center of the ring, and the ring lying in the xy plane.
Linear mass density:
R de
λ =
Differential mass:
de
R
0
Hint : x = R cos0 ; y = R sine
X
dm
M
2πR
=
XRd0 = d0
2π
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