The parallel axis theorem for the area moment of inertia of a shape states that the difference between the moments of inertia between an arbitrary axis in space, and a parallel axis passing through the centroid of the shape, is equal to the area of the shape multiplied by the square of the distance between the two axes. Hence, the moment of inertia is a tensor quantity – it has different values about different axes in the two or three-dimensional space. The moment of inertia can be measured for both two-dimensional and three-dimensional objects. Objects of different dimensions will have different moments of inertia about the same axis as well. The reason for this will be explained more descriptively in the section on the parallel axis theorem. The same object will have vividly different moments of inertia about different axes. The main quantities required to measure the moment of inertia of an object are the dimensions of the object and the axis about which the moment of inertia is to be measured. Depending upon the shape of the object, the larger the dimensions of an object, the greater will be the moment of inertia. Known as the area moment of inertia or the second moment of inertia, the mathematical moment of inertia is used to describe the distribution of points in a shape about an arbitrary axis. However, this moment of inertia is different. A large object has greater inertia and is hence more difficult to move or stop as compared to a small object. The inertia of an object is what provides the object resistance to change in its state of rest or motion. You might remember from your physics class about the concept of inertia. The moment of inertia is a quantity that provides a numerical description of the ease of rotation of a body about a particular axis. What are the applications of the moment of inertia?.
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