16.1 : 惯性矩和惯性积

The moment of inertia for a differential element of a rigid body can be calculated by multiplying the mass of the element by the square of the shortest distance from any one of the three-coordinate axes to the element.

By integrating this expression over the entire mass of the body, the moment of inertia of the body can be determined.

Similarly, the moment of inertia about the other two axes can be found. The moment of inertia is always a positive quantity.

Additionally, the product of inertia for a differential element in relation to a pair of perpendicular planes is defined as the product of the mass of the element and the perpendicular distance from the plane to the element.

Integrating this over the entire mass, the product of the inertia of the body is calculated. The product of inertia can be positive, negative, or zero.

If the mass is symmetric about one or both orthogonal planes, then the product of inertia about such planes is always zero.