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Circular Motion & Rotational Dynamics

Formulae For The Moment of Inertia of Regular Bodies

Shape of body Axis of Rotation Figure Moment of Inertia (I) Radius of Gyration (K)
(1) Circular Ring, M :- Mass, R :- Radius 1)Passes through the centre and perpendicular to the plane MR2 R
2) About its Diameter in its own plane R / √2
3) About a tangential axis perpendicular to its own plane. 2MR2 √2R
4) About a tangential axis in its own plane MR2 .R
(2) Circular disc, M:- Mass, R:- Radius 1) Passing through the centre and perpendicular to the plane
2) About Diameter MR2/4 MR2 R
4) About a tangential axis Perpendicular to its own plane MR2 R
3) Hollow Cylinder, M = Mass, R = Radius, L = Length a) About its geometrical axis MR2 R
b) About an axis passing through its CM and perpendicular to its length
c) About an axis perpendicular to its length and passing through one end of the cylinder
(4) Solid Cylinder, M:- Mass, R:- Radius, L:- Length A) About its geometrical Axis
B) About an axis passing through its C.G. and Perpendicular to its axis
C) About the diameter of one of the faces of the cylinder and perpendicular to the length
(5) Solid Sphere, M:- Mass, R:- Radius A) About its axis OR diameter, which is passing through centre.
B) About Tangential axis
(6) Thin Spherical Shell (Hollow Sphere), M: Mass, R: Radius, Thickness negligible 1) Passing through axis or diameter
2) About Tangential Axis
(7) Solid sphere with cavity, Internal radius = r, Outer Radius = R, Mass :- M About passing through centre OR about diameter

(8) Thin rod [thickness is negligible w.r.t. length] 1) Passing through centre of mass and perpendicular to length

2) Passing through its one end and perpendicular to axis.
(9) Rectangular plate, a = Length, b = width, M = Mass (a) About an axis passing through CM and perpendicular to side a in its plane.
b) about an axis passing through CM and perpendicular to side b in its plane.
c) About an axis passing through CM and


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