Moment of Inertia

In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass (SI units kg·m2, US units lb_m ft2), is a property of a distribution of mass in space that measures its resistance to rotational acceleration about an axis. Newton's first law, which describes the inertia of a body in linear motion, can be extended to the inertia of a body rotating about an axis using the moment of inertia. That is, an object that is rotating at constant angular velocity will remain rotating unless acted upon by an external torque. In this way, the moment of inertia plays the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular acceleration. The symbols I and sometimes J are usually used to refer to the moment of inertia or polar moment of inertia.

The moment of the inertia force on a particle around an axis multiplies the mass of the particle by the square of its distance to the axis, and forms a parameter called the moment of inertia. The moments of inertia of individual particles sum to define the moment of inertia of a body rotating about an axis. For rigid bodies moving in a plane, such as a compound pendulum, the moment of inertia is a scalar, but for movement in three dimensions, such as a spinning top, the moment of inertia becomes a matrix, also called a tensor.

In 1673 Christiaan Huygens derived the equation for the center of oscillation and oscillation period of compound pendulums, thus making use of the general equation for the moment of inertia for the first time. The term moment of inertia was introduced by Leonhard Euler in his book Theoria motus corporum solidorum seu rigidorum in 1765. In this book, he discussed the moment of inertia and many related concepts, such as the principal axis of inertia.