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firebottoday at 12:50 AM1 replyview on HN

Because it's not momentum. ;p

F=ma (Force equals mass times acceleration)

W=Fd (work equals force multiplied by distance)

V^2=2ad (velocity squared equals two times acceleration times distance)

So W = Fd = ma(v^2/2a)

Finally: W=1/2mv^2 (work equals 1/2 mass times velocity squared)

So this explains why car crashes can be so dramatic, as a doubling of speed results in 4x the kinetic energy.


Replies

ajrosstoday at 12:56 AM

Actually, it is momentum, sorta. Galilean 3D momentum isn't conserved under special relativity. The energy-momentum four-vector, however, is, under all lorentz-transformed frames.

So in some sense energy is momentum in the time direction (though it's not a Euclidean 4D space, so beware of assumptions). For an object at rest, this becomes its E=mc² equivalence. Kinetic energy is just a straightforward "rotation" of the frame.

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