Centre of mass and moment of inertia

The centre of mass of a solid object is the point where the mass of the object can be considered to be concentrated for many physical purposes. The moment of inertia measures how difficult it is to rotate an object about a certain axis; it depends on how the mass is distributed relative to that axis.

Important properties

• The centre of mass of a system of points (or masses) is the weighted average of their positions.

• For a uniform solid, the centre of mass is at its geometric centre.

• The moment of inertia increases as mass is distributed farther from the axis of rotation.

• For point masses, the moment of inertia about an axis is the sum of $m_i r_i^2$, where $m_i$ is the mass and $r_i$ is the distance to the axis.