# Rotation Around A Fixed Axis - Dynamics - Moment of Inertia

Moment of Inertia

The moment of inertia of an object, symbolized by I, is a measure of the object's resistance to changes to its rotation. The moment of inertia is measured in kilogram metre² (kg m²). It depends on the object's mass: increasing the mass of an object increases the moment of inertia. It also depends on the distribution of the mass: distributing the mass further from the centre of rotation increases the moment of inertia by a greater degree. For a single particle of mass a distance from the axis of rotation, the moment of inertia is given by

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... In order to compare formulations of the inertia matrix in terms of a product of skew-symmetric matrices and in terms of a tensor formulation, the following identities are useful ... the skew symmetric matrix associated with the position vector R=(x, y, z), then the product in the inertia matrix becomes This product can be computed using the matrix formed by the outer product using the ...
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... In classical mechanics, moment of inertia, also called mass moment, rotational inertia, polar moment of inertia of mass, or the angular mass, (SI units kg·m²) is a measure of an object's resistance to changes to its ... It is the inertia of a rotating body with respect to its rotation ... The moment of inertia plays much the same role in rotational dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular velocity, torque and angular ...

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