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nna
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for a system of particles why is centre of mass independent of the origin?
The Centre of Mass (COM) of a system of particles is a point that represents the average position of the mass of the entire system. It is the point where the total mass of the system can be considered to be concentrated.
The COM is important because it allows us to simplify the analysis of a system of particles by considering it as a single point with a certain mass and location. This makes it easier to determine the overall motion and behavior of the system.
The COM is calculated by taking the weighted average of the positions of all the particles in the system, with the mass of each particle as the weight. This can be expressed as COM = (m1r1 + m2r2 + ... + mnrn) / (m1 + m2 + ... + mn), where m is the mass and r is the position vector of each particle.
No, the COM does not always lie on the system's axis of symmetry. It depends on the distribution of mass within the system. If the mass is evenly distributed, then the COM will lie on the axis of symmetry. But if the mass is unevenly distributed, the COM may be located off the axis of symmetry.
Yes, the COM can be located outside of the system if the particles are arranged in such a way that the weighted average of their positions results in a point outside of the system's boundaries. This can happen if there is a large concentration of mass in one area and a small concentration in another area.