Class 11 Physics Rotational Motion Theorem of parallel axis

Theorem of parallel axis

  • 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 the square of the distance between the two parallel axes.

  • This theorem is applicable to a body of any shape.

 

Example:  Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2/4, find its moment of inertia about an axis normal to the disc and passing through a point on its edge

Solution:


We can apply Perpendicular axis theorem here on x axis & y axis and get I’, moment of inertia in z axis.
Iz = Ix + Iy , now as because of symmetry Ix & Iare same so Iz = I’ = 2I = Mr2/2

Now we can apply parallel axis theorem to find I’’.
I’’ = I’ + MR2 = 3/2(MR2)

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