Moment of Inertia in different bodies

Different rigid bodies have different values of the moment of inertia and hence different formulas to calculate it. Also, the Moment of Inertia in a body depends upon the axis of rotation. So here is a table of moment of inertia in different bodies depending upon the axis of rotation.

S.N	Rigid Body	axis of rotation	Moment of Inertia
1.	thin rod	perpendicular to its plane and passing through a center	$I = \frac{1}{12}ML^2$
2.	thin rod	perpendicular to its plane and passing through one end	$I = \frac{1}{3}ML^2$
3.	circular ring	perpendicular to its plane and passing through a center	$I = MR^2$
4.	circular ring	about any diameter	$I = \frac{1}{2}MR^2$
5.	circular ring	in a plane about any tangent	$I = \frac{3}{2}MR^2$
6.	circular disk	perpendicular to its plane and passing through a center	$I = \frac{1}{2}MR^2$
7.	circular disk	about any diameter	$I = \frac{1}{4}MR^2$
8.	circular disk	about any tangent in a plane	$I = \frac{5}{4}MR^2$
9.	rectangular lamina	perpendicular to its plane and passing through its center	$I = \frac{1}{12}M\left(l^2 + b^2 \right)$
10	rectangular lamina	axis along the edge of the length	$I = \frac{1}{3}Mb^2$
11.	solid sphere	through its center	$I = \frac{2}{5}MR^2$
12.	solid sphere	about any tangent	$I = \frac{7}{5}MR^2$
13.	hollow sphere	through its center	$I = \frac{2}{3}MR^2$
14.	hollow sphere	about any tangent	$I = \frac{5}{3}MR^2$
15.	solid cylinder	about any symmetry axis	$I = \frac{1}{2}MR^2$
16.	hollow cylinder	about its axis	$I = MR^2$

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