
Angular Momentum of a Rigid Body
A rigid body is both rotating about its center of mass and translating with respect to the origin of the reference frame, O shown in Figure 1. From [1] of Angular Momentum  System of Particles and Figure 1, the angular momentum of a particle composing the rigid body is
where m = the mass of the particle, r_{CM} = the position of the body's CM, v_{CM} = the velocity of the body's CM, r = the position of the particle, r' = the relative position of the particle to the body's CM, v = the velocity of the particle, and v' = the relative velocity of the particle to the body's CM. Since all the particles in the body experience the same angular velocity, [1] can be rewritten to
since, from Figure 1,
where w = the angular velocity of the body. The angular momentum of the body is the sum of the angular momentums of the particles composing the body:
where M = the mass of the rigid body. From [4] of Inertia Tensor and [4]:
where p_{CM} = the momentum of the body, I_{CM} = the inertia tensor of the body about its CM, H_{CM} = the angular momentum of the body due to the motion of the CM, and H' = the angular momentum of the body due to its rotation about the CM. As shown in [5], the angular momentum of a rigid body can be reduced to two distinct terms: the angular momentum due to the translation of the body's CM (H_{CM}), and the angular momentum due to the rotation of the body about its CM (H'). The first term in [5] is called the remote term, while the second is the local term of the body's angular momentum:

© YoungHoo Kwon, 1998 