General Mechanics/Rigid Bodies

__NOTOC__ If the set of particles in the previous chapter form a rigid body, rotating with angular velocity ω about its centre of mass, then the results concerning the moment of inertia from the penultimate chapter can be extended. We get where (rn1, rn2, rn3) is the position of the nth mass. In the limit of a continuous body this becomes where ρ is the density. Either way we get, splitting L into orbital and internal angular momentum, and, splitting T into rotational and translational kinetic energy, It is always possible to make I a diagonal matrix, by a suitable choice of axis. Mass Moments Of Inertia Of Common Geometric Shapes The moments of inertia of simple shapes of uniform density are well known. Spherical shell mass M, radius a Solid ball mass M, radius a Thin rod mass M, length a, orientated along z-axis Disc mass M, radius a, in x-y plane Cylinder mass M, radius a, length h orientated along z-axis Thin rectangular plate mass M, side length a parallel to x-axis, side length b parallel to y-axis further reading Statics/Moment of Inertia (contents) Statics/Geometric Properties of Solids