Moment of inertia
lastmod 2020-09-20created 2020-09-201 edits
The moment of inertia (慣性-) is a physical quantity that expresses how strongly an object tends to maintain its rotational motion, and it corresponds to mass in linear motion. Its symbol is usually the capital Latin letter \(I\), though it is sometimes written as \(J\). The moment of inertia plays a very important role in rotational motion, because it is the physical quantity that ties together the relationships among angular momentum, angular velocity, angular acceleration, and torque, which are essential for describing rotational motion.
There are two ways to express the moment of inertia: the scalar moment of inertia, expressed as a scalar, and the moment of inertia tensor, expressed as a higher-order tensor, or simply the inertia tensor. The scalar moment of inertia is often just called the moment of inertia. For simple rotations, the scalar moment of inertia alone is enough to describe the relationships among the physical quantities, without the more complex inertia tensor. However, the scalar moment of inertia cannot describe the relationships among physical quantities for complex rotations such as a spinning top or a gyroscope, so in such cases the inertia tensor is used to describe them.
The first person to use the concept of the moment of inertia was Leonhard Euler. The concept first appeared in his book Theory of the Motion of Solid or Rigid Bodies, published in 1730, and several related concepts, such as the principal axes of the moment, were introduced through this book.