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Moment of inertia of rigid body about an axis, where r is the distance from that axis and is the density:
I = dm r2 = dxdydz r2
(for comprehensive lists of moments of inertia of specific bodies, see See Also)
Moment of momentum (angular momentum) about centre of mass, C:
LC=IC (principal axis case)
LC=IC (general case)
where is parallel to a principal axis, with principal moment of inertia I, and is the moment of inertia tensor.
About a general point, P:
LP=IC + PC mvC (principal axis case)
LP=IC + PC mvC (general case)
Kinetic Energy:
KE = 12mv2C + KErot = KEtrans + KErot, where:
KErot=12 LC=12 IC2 (principal axi