There is a geometric way one can show the relation between kinetic energy and momentum which is a mathematical curiosity in my opinion. Let the mass of an object be equal to 2 PI. Then:(adsbygoogle = window.adsbygoogle || []).push({});

P = 2 pi v

KE = 1/2 (2 pi ) v sq

or

KE = pi v sq

Hence, graphically, if we set v = r, where r is the radius of a circle, we have a circle whose circumference is momentum, 2 pi v, and whose area is the kinetic energy, pi v sq. Thus, for the case where the mass is 2 pi, we see the kinetic energy is geometrically bounded by the momentum of the object. Interesting.

Wonder what would happen to this circle at relativistic velocities?

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# Pi, momentum, and kinetic energy

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