Does the Center of Mass Change with Interaction Type or Reference Frame?

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The center of mass (CM) of a system of particles remains invariant regardless of whether the particles are interacting or non-interacting. The position of the CM does not change when transitioning between different inertial or non-inertial reference frames. This invariance holds true as long as the same system of particles is considered. The discussion emphasizes that the CM is consistent across various frames of reference. Overall, the CM is a fundamental property that is unaffected by the interactions between particles or the choice of reference frame.
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Homework Statement



Does the CM of a system of particles depend on whether the particles are interacting or non-interacting?Will the positon of CM change in another inertial or non-inertial frame?

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The Attempt at a Solution



My attempts:Please check.
CM is invariant -no matter whether the particles are interacting or non-interacting-whether ther is a relative motion or not within the system as long as we are dealing with the same system of particles.

CM of a system of particles can be shown to be invariant w.r.t. any origin of an arbitrary reference frame.So,it must be the same even in an inertaial or non-inertial frame of reference.
 
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