Moment of inertia, also called mass moment of inertia or the angular mass, is a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass. That is, it is the inertia of a rigid rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in basic dynamics, determining the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities. While a simple scalar treatment of the moment of inertia suffices for many situations, a more advanced tensor treatment allows the analysis of such complicated systems as spinning tops and gyroscopic motion.
The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. For example, consider two discs, A and B, made of the same material and of equal mass. Disc A is larger in diameter but thinner than B. It requires more effort to accelerate disc A (change its angular velocity) because its mass is distributed farther from its axis of rotation: mass that is farther out from that axis must, for a given angular velocity, move more quickly than mass closer in. In this case, disc A has a larger moment of inertia than disc B.
The moment of inertia of an object can change if its shape changes. A figure skater who begins a spin with arms outstretched provides a striking example. By pulling in her arms, she reduces her moment of inertia, causing her to spin faster....
Source: Wikipedia
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