Particles of mases m,2m,3m and 4m are held in a rigid light framework at points (0,1,1),(1,1,0) and (-1,0,1) respectively.show that the moment of inertia of the system about the x_axis,y_axis and z_axis are 13,16 and 15 respectively(in appropriate units)
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ANSWER
∵x
CM
=
m+2m+...+nm
mL+2m×2L+...+nm×nL
=
(1+2+...+n)
L(1
2
+2
2
+...+n
2
)
=L
∑n
∑n
2
=L
2
n(n+1)
6
n(n+1)(2n+1)
=
3
(2n+1)L
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