Angular momentum of a rigid body

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The angular momentum of a rigid body can be analyzed in both inertial and body coordinate systems. In the body system, the rigid body appears at rest, yet it can still possess non-zero angular momentum. This is because the body system is defined such that the center of mass remains at the origin, (0,0,0), rather than rotating with the body itself. The distinction between these coordinate systems is crucial for understanding angular momentum in rigid bodies. Thus, angular momentum can exist even when the body is not in motion relative to its own coordinate system.
karlo1961
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The angular momentum of a rigid body is often calculated into different coordinate systems. One is an inertial system and the other is a body system moving with the rigid body. Now, in the body system the rigid body is at rest and has no movement at all. How is it that it can still have a non-zero angular momentum the body system.
 
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Typically, the "system moving with the rigid body" is a system in which the center of mass is always at (0,0,0), not one that is rotating with the body!
 

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