Inertimomentet

Inertimomentet is the term used in physics to denote the moment of inertia, a property that quantifies an object’s resistance to changes in its rotational motion about a chosen axis. It depends on how the object's mass is distributed relative to that axis.

For a discrete system of masses, inertimomentet is I = sum m_i r_i^2, where r_i is the perpendicular distance from the axis. For a continuous body, I = ∫ r^2 dm, with dm representing an infinitesimal mass element. In three dimensions, the moment of inertia is part of the inertia tensor, and the scalar I_axis is obtained by projecting the tensor along the rotation axis.

The value of inertimomentet depends on the axis of rotation. The parallel axis theorem relates moments about different axes: I = I_cm + M d^2, where I_cm is the moment about an axis through the center of mass, M is the total mass, and d is the distance between the axes.

Common results for simple shapes about central axes include: a solid cylinder or disc: I = (1/2) M R^2; a solid sphere: I = (2/5) M R^2; a thin circular hoop: I = M R^2, with R as radius. These expressions illustrate how more mass concentrated away from the axis increases inertimomentet.

Applications of inertimomentet span mechanical engineering, rotor dynamics, gyroscope design, and planetary science, where it informs rotational behavior and density distribution. It is typically determined from geometry, material density, or by experiments using torsional oscillations or controlled torques. In many languages, including Swedish, the term is also called tröghetsmomentet.