In uniform circular motion, the particle moves along a circular path at constant speed. For such a particle, angular momentum is conserved about any point in the plane of the circle if no external torques act on the system; thus, the angular momentum is constant about any point in the plane of the circle.

The conservation of angular momentum is one of the principles in physics. According to it, if there is no external torque acting on the system, its angular momentum will be conserved. For a uniform circular motion, the motion of the particle is restricted to a plane and the forces that act upon it are internal to the system. Thus, its angular momentum will be conserved about any point within that plane.

It should be noted that even though the angular momentum is conserved about points that are inside the plane of the circle, the value of the angular momentum is dependent on the selection of the reference point. On the other hand, the reason that it remains conserved about any point in the plane results directly from the lack of external torques.

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