Mass-Energy

Discussion

relativistic momentum

p = mv
√(1 − v2/c2)

relativistic energy

E = mc2
√(1 − v2/c2)

binomial expansion (or taylor series)

E = mc2  ⎛
⎝		 1 +  1   v2  +  3   v4  +  5   v6  +  35   v8  +  63   v10  + … ⎞
⎠
2 c2 8 c4 16 c6 128 c8 256 c10

the first term is the rest energy

E = mc2

the second term is the classical formula for kinetic energy

K = m  1  v2
2

the higher order terms are corrections that become more and more noticeable as the speed approaches the speed of light

relativistic mass

m' = m
√(1 − v2/c2)

for massed particles

E2 = p2c2 + (mc2)2

for massless particles

E = pc

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