what is moment of inertia

The moment of inertia, also known as the mass moment of inertia or rotational inertia, is a property of a rigid body that determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the bodys mass distribution and the axis chosen, with larger moments requiring more torque to change the bodys rate of rotation by a given amount. The moment of inertia is an extensive (additive) property, and for a point mass, it is simply the mass times the square of the perpendicular distance to the axis of rotation. For an extended rigid body, the moment of inertia is the sum of all the small pieces of mass multiplied by the square of their distances from the axis of rotation. It is defined as the product of the mass of a section and the square of the distance between the reference axis and the centroid of the section. The moment of inertia is crucial in determining how difficult it will be to angularly accelerate something and is a key factor in the angular version of Newtons second law. The unit of moment of inertia is a composite unit of measure, and it is commonly calculated using integral calculus for bodies with shapes that can be described by a mathematical formula.