Question

State the theorems of parallel axis and perpendicular axis of moment of inertia

Answer 1

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


Theorem of perpendicular axes : The Moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of its moment of inertia about the mutually perpendicular axes concurrent with perpendicular axis and lying in the plane of the laminar body.

Answer 2

The theorem of parallel axis states that the moment of inertia of a body about any axis is equal to its moment of inertia about a parallel axis through its centre of mass + the product of mass M of the body and the square of the perpendicular distance " a" between the two axes
I(net) = I(cm) + Ma²
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The theorem of perpendicular axes states that the moment of inertia of a uniform plane lamina about an Axis perpendicular to its plane is equal to the sum of its moment of inertia about any two mutually perpendicular Axes in the plane intersecting on the first axis.