Conservation of energy in a CM system moving at constant velocity

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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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kuruman
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In what situation? I don't see anything wrong with that except for the lack of parentheses where they belong.
 
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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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