Physics > Basics of Rotational Motion > 6.0 Theorems of moment of inertia

  Basics of Rotational Motion
    1.0 Rigid body
    2.0 Motion of rigid body
    3.0 Kinematics of a plane motion
    4.0 Moment of inertia
    5.0 Radius of gyration $(K)$
    6.0 Theorems of moment of inertia
    7.0 Moment of inertia of uniform continious rigid bodies

6.1 Parallel-axis theorem
The moment of inertia of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of mass and the product of its mass and square of the distance between the two parallel axes.

Mathematically, $$I = {I_{COM}} + M{d^2}$$
where,
${I_{COM}}$: Moment of inertia about an axis passing through centre of mass (COM) and parallel to an axis of $I$
$I$: Moment of inertia about any given axis
$d$: Perpendicular distance between the two parallel axes
$M$: Mass of the rigid body
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