Rigid body
A collection of particles such that the distance between any two particles is fixed: is constant for every pair .
Definition 5.1 (Rigid Body)
A rigid body is a collection of particles such that the distance between any two particles is fixed.
Translations and rotations
The only motions a rigid body can undergo are translations of the centre of mass, and rotations. A rotation is described by an angular velocity vector , where points along the axis of rotation and is the angular speed of rotation, with direction determined by the right hand rule:
where is the position relative to some (any) point on the axis of rotation, since there are infinitely many parallel axes an object can rotate about.
Rotation preserves distances
In a rigid body all particles rotate with the same angular velocity,
and this keeps the distances between particles fixed:
Related
Stated in
- Definition 5.1 (Rigid Body)§5 Rigid Bodies