## Wednesday, February 24, 2016

### Moment of Inertia of Solid Sphere, Halo Sphere and Thin Rod

Moment of Inertia of solid sphere

Let us consider a body in three dimensions. Let the body is a sphere and let it has some known mass and the known radius. Let we have mathematically measured the moment of inertia of the sphere about an axis passing through the center and is perpendicular to the plane.

Once if this moment of inertia is known to you about one axis, we can measure the moment of inertia about a parallel axes and perpendicular axes theorems as shown in the video below in detail further.

Moment of Inertia of Halo Sphere

Halo sphere is also a three dimensional body who has cavity or emptiness in the middle portion of the sphere. In comparison with solid sphere of same mass and radius, it can be proved that the moment of inertia of halo sphere is more than that of the solid sphere. It is simply because of radius of gyration of the halo sphere is more than that of the solid sphere. Radius of gyration is the effective distance of the body where its mass is concentrated from the axis of rotation.

If the body starts rotating from a different axis, we can find its moment of inertia using parallel axes and perpendicular axes theorem as shown in the video lecture below.

Moment of inertia of thin rod

A thin rod is again one dimensional body and its mass is directly proportional to length of the body. We can measure the moment of inertia of this rod about an axis passing through the center of the rod and perpendicular plane using integration method.

As the axis of rotation changes, its moment of inertia of changes. To find the moment of inertia of the rod about a different axis, we can use parallel axis theorem as shown in the video lesson.

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