Mass moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation.
Mass moment of inertia is specifically used to calculate rotational motion, while moment of inertia can refer to both rotational and linear motion. Mass moment of inertia takes into account the distribution of mass around an axis of rotation, while moment of inertia only considers the mass of an object.
The mass moment of inertia can be calculated using the parallel axis theorem, which states that the mass moment of inertia of an object is equal to the sum of its moment of inertia about its center of mass and the product of its mass and the square of the distance between the two axes.
The mass moment of inertia is directly proportional to the angular acceleration of an object. This means that as the mass moment of inertia increases, the angular acceleration decreases, and vice versa.
The mass moment of inertia affects the work done by gravity on an object by determining the amount of torque needed to rotate the object. The greater the mass moment of inertia, the more torque is required, and therefore, the more work is done by gravity on the object.