If velocity is a relative term then a body would possess different Kinetic Energy in different frames of reference. How can a body have different energies simultaneously for different observers ?
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$\begingroup$ A quantity whose rules you know how it transforms is called covariant vs invariant. It is just as good to know a quantity in one frame and the rules for its changes as it is to know it in all frames. $\endgroup$– AHusainCommented Jul 23, 2017 at 4:10
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$\begingroup$ See this answer to a somewhat different question. physics.stackexchange.com/a/94290/37364 $\endgroup$– mmesser314Commented Jul 23, 2017 at 4:59
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$\begingroup$ Related: "Galilean invariance of Lagrangian for non-relativistic free point particle?" physics.stackexchange.com/q/14875/226902 See also: physics.stackexchange.com/q/287101/226902 $\endgroup$– QuilloCommented Mar 9, 2023 at 14:52
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1 Answer
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Not a full answer, but just a thought experiment for you to chew on.
Consider a person on a train, maybe they're eating an apple. You're not on the train. You calculate the kinetic energy of the apple - it's maybe a 0.1kg mass, moving at over 100 km/h. That's a lot of kinetic energy. Now swap back into the frame of the person on the train. You'd better hope it doesn't have the same kinetic energy, or eating that apple is going to be quite problematic.
The point of this thought experiment, is that like velocity, kinetic energy is something that's frame dependent. It's just a quantity that simplifies understanding of the dynamics in a certain inertial frame.
