Is angular momentum about all points same if the body is rigid and is rotating/translating/rolling with a constant velocity? Why? No external force is acting on the body.
Answer
This is a surprisingly deep question, because to answer it you need to understand the basic reason conservation laws exist. There is a theorem by the mathematician Emmy Noether, and known not unreasonably as Noether's theorem, that tells us conservation laws are related to symmetry.
Conservation of linear momentum is related to translation symmetry. This says that if we move a system some distance in space and the laws of physics are unchanged then linear momentum will be conserved. So if we choose a point for our origin, then measure the momentum of some system, moving our origin will not change the linear momentum.
Conservation of angular momentum is related to rotational symmetry. This says that if we rotate our system by some arbitrary angle and the laws of physics are unchanged then angular momentum will be conserved. So if we choose an origin and some axes, then measure the momentum of some system, rotating our axes will not change the angular momentum.
However angular momentum is not constant under a translation. If we move our origin and recalculate the angular momentum there is no reason to expect that the angular momentum will be conserved, and indeed it isn't.
I should clarify what I mean by the laws of physics are unchanged. Any system can be described by an equation called the Lagrangian, and from the Lagrangian we can calculate the equations of motion of the system. When I say the laws of physics aren't changed by a translation I mean the Lagrangian is not changed by the translation, or likewise for rotation that the Lagrangian is unchanged by the rotation.
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