As for the moment of inertia of irregular rigid bodies or uneven rigid bodies, it is generally measured by experimental methods, so experimental methods are very important. Moment of inertia is used for dynamic calculation of various motions of rigid bodies.
The expression of moment of inertia is
If the mass of a rigid body is continuously distributed, the formula for calculating the moment of inertia can be written as follows
Extended data:
Related Theorems of Moment of Inertia
Parallel axis theorem
Parallel axis theorem: Let the mass of the rigid body be m, the moment of inertia of the axis around the center of mass be Ic, and move this axis in any direction by a distance d, then the moment of inertia around the new axis is:
This theorem is called the parallel axis theorem.
perpendicular axis theorem
Perpendicular axis theorem: The moment of inertia of a plane rigid thin plate around an axis perpendicular to its plane is equal to the sum of moments of inertia around any two orthogonal axes intersecting with the vertical axis in the plane.
Expression:
In addition to the above two theorems, the continuation rule is also commonly used. The continuation law stipulates that if any point of an object is displaced in parallel along a straight axis of any size, the moment of inertia of the object around this axis remains unchanged. As you can imagine, an object, parallel to the straight axis, is pulled away at both ends.
When an object is stretched, the vertical distance from any point of the object to the straight axis is kept constant, and the stretching law makes it clear that the moment of inertia of the object on this axis is unchanged. The generalized rule can be simply obtained from the definition of moment of inertia.
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