# Moment of inertia

Quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration.

- Moment of inertia234 related topics

## Flywheel

A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed.

## Tensor

Components stress tensor.svg (.

Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), or general relativity (stress–energy tensor, curvature tensor, ...) and others.

## Aircraft principal axes

Free to rotate in three dimensions: yaw, nose left or right about an axis running up and down; pitch, nose up or down about an axis running from wing to wing; and roll, rotation about an axis running from nose to tail.

These axes are related to the principal axes of inertia, but are not the same.

## Angular momentum

Rotational analog of linear momentum.

Because angular momentum is the product of moment of inertia and angular velocity, if the angular momentum remains constant (is conserved), then the angular velocity (rotational speed) of the skater must increase.

## Moment (mathematics)

In mathematics, the moments of a function are quantitative measures related to the shape of the function's graph.

If the function represents mass, then the first moment is the center of the mass, and the second moment is the rotational inertia.

## Torque

Newton-metre .

The definition of torque states that one or both of the angular velocity or the moment of inertia of an object are changing.

## Rigid body

Solid body in which deformation is zero or so small it can be neglected.

The angular momentum with respect to the center of mass is the same as without translation: at any time it is equal to the inertia tensor times the angular velocity. When the angular velocity is expressed with respect to a coordinate system coinciding with the principal axes of the body, each component of the angular momentum is a product of a moment of inertia (a principal value of the inertia tensor) times the corresponding component of the angular velocity; the torque is the inertia tensor times the angular acceleration.

## Rigid body dynamics

In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces.

where M is the total mass and IC is the moment of inertia about an axis perpendicular to the movement of the rigid system and through the center of mass.

## Moment (physics)

Mathematical expression involving the product of a distance and physical quantity.

In 1765, the Latin term momentum inertiae (English: moment of inertia) is used by Leonhard Euler to refer to one of Christiaan Huygens's quantities in Horologium Oscillatorium.

## Radius of gyration

Radius of gyration or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there.