Classical Physics - Moment Of Inertia

Moment Of Inertia

Moment of inertia plays the same role in rotational motion as mass in linear motion. Moment of inertia I = ∑m_ir₁²,

I = ∫r² dm for continuous distribution of mass

I = M K²

Where M is the mass of the body and k is radius of gyration MOI is a tensor quantity.

Moment of inertia of bodies about an axis passing through their centre of mass (COM) and perpendicular to the plane of the body are given as 

MOI of a ring = mr2

MOI of a disc (solid) mr² / 2

MOI of a disc (annular) = m / 2 (r₁² + r₂³)

MOI of a cylinder (solid) = mr² / 2 

MOI of a hollow cylinder = mr² (if shell type)

= m / 2 (r²₁ + r²₂)

MOI of a sphere (shell) = 2 / 3 mr²

MOI of a solid sphere = 2 / 5 mr²

MOI of a hollow sphere = 2 / 5 m (r²₁ + r²₃)

MOI of a rod (cylindrical) = mI² / 12 

 MOI of a rectangular rod = M (I² + b²) / 12 

MOI of a rectangular lamina = m ( I² + b²) / 12

MOI of a ring about one of the diameter is mr² / 2

MOI of a disc about one of the diameters is I = mr² / 4

MOI of a cylindrical rod about the edge is mI² / 3  

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