Conservation of energy in a CM system moving at constant velocity

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SUMMARY

The discussion centers on the application of the conservation of energy in a center of mass (CM) system moving at constant velocity, specifically using the equation ##1/2m_1v_{1c}^2+1/2m_2v_{2c}^2=1/2m_1v_{1c}'^2+1/2m_2v_{2c}'^2##. It is established that while kinetic energy (KE) is frame-dependent, energy conservation remains valid across all frames. The key takeaway is that energy is conserved in a moving system, despite variations in kinetic energy measurements from different observers.

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Leo Liu
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My book uses ##1/2m_1v_{1c}^2+1/2m_2v_{2c}^2=1/2m_1v_{1c}'^2+1/2m_2v_{2c}'^2## to show that the angles of deflection of the collision between two particles are the same in the centre of mass frame. However, I am doubtful that one can apply the conservation of energy to a "moving" system because the kinetic energies of the same object measured at different observers are different. Is this method valid?
 
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In what situation? I don't see anything wrong with that except for the lack of parentheses where they belong.
 
Leo Liu said:
I am doubtful that one can apply the conservation of energy to a "moving" system because the kinetic energies of the same object measured at different observers are different. Is this method valid?
Frame invariant and conserved are two completely independent concepts. KE is frame variant, it has different values in different frames. But in all frames energy is conserved, its value stays the same over time.
 
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