Moment of inertia of rigid body about an axis, where r is the distance from that axis and 蟻 is the density:
I = 鈭玠m r2 = 鈭乨xdydz 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蠅 (principal axis case)
LC=I藴C蠅 (general case)
where 蠅 is parallel to a principal axis, with principal moment of inertia I, and 脦 is the moment of inertia tensor.
About a general point, P:
LP=IC蠅 + PC鈨� 脳mvC (principal axis case)
LP=I藴C蠅 + PC鈨� 脳mvC (general case)
Kinetic Energy:
KE = 12mv2C + KErot = KEtrans + KErot, where:
KErot=12 蠅鈰匧C=12 IC蠅2 (principal axi
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