The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the axis. The further out the object's mass is, the more rotational inertia the object has, and the more torque (force* distance from axis of rotation) is required to change its rotation rate.
The moment of inertia is a measure of an object's resistance to rotational motion. It is a property of an object that depends on its mass distribution and the axis of rotation.
The moment of inertia is calculated by summing the mass of each individual particle in an object, multiplied by the square of its distance from the axis of rotation. This can be expressed mathematically as I = Σmr², where I is the moment of inertia, m is the mass of the particle, and r is the distance from the axis of rotation.
The moment of inertia is a general term that refers to an object's resistance to rotational motion. Mass moment of inertia specifically refers to the moment of inertia of a rigid body, which is calculated by considering the mass distribution of the object and its distance from the axis of rotation.
The moment of inertia is affected by both the mass distribution of an object and the axis of rotation. Objects with more mass concentrated farther from the axis of rotation will have a larger moment of inertia, while objects with more mass closer to the axis of rotation will have a smaller moment of inertia.
The moment of inertia plays a crucial role in rotational motion and is essential for understanding how objects behave when subjected to torque. It is also used in various engineering applications, such as designing rotating machinery and calculating the stability of structures.