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This question already has an answer here:

The speed of an Alpha particle is: 10^7 m/s.

This is a speed approaching the speed of light. hence, should the (relativitic) mass of the Alpha particle vary?

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marked as duplicate by Gert, John Rennie, Kyle Kanos, user10851, ACuriousMind Nov 19 '15 at 0:10

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  • $\begingroup$ The relativistic mass increases by a factor of 1.006 compared to its rest mass. $\gamma=\frac{1}{sqrt(1-\frac{v^2}{c^2})}$ $\endgroup$ – Timeless Nov 18 '15 at 14:16
  • $\begingroup$ No, this is wrong. See comment to answer below. $\endgroup$ – Gert Nov 18 '15 at 15:12
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    $\begingroup$ BTW, Aman, $10^7\,\mathrm{m/s}$ is about 3% of $c$, so it is mildly relativistic but I would not characterize it as "approaching the speed of light". $\endgroup$ – dmckee Nov 18 '15 at 15:54
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According to the special relativity, there is a formula describing the relation of particle mass with its speed: $$m = {m_0 \over \sqrt {1- ({v \over {c}})^2}}$$ where $m_0$ is the mass of the particle when it is still----rest mass.

So as long as a particle moves, no matter how large or small the velocity is, the mass of the particle $m$ will vary and be different from its rest mass $m_0$.

If $v$ is small, the change in mass is very small. In this case, the ignorance of the change in mass is a good approximation for describing the system you are concerned, that is, back to Newton's world---the mass of a particle is constant. On the other hand, if $v$ is so large that it can be comparable with the speed of light, the change in mass is remarkable. So in this case, we must take the variance of the particle mass into consideration!

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  • $\begingroup$ No, this is wrong. Widely believed but nonetheless wrong. It's momentum and kinetic energy that vary relativistically when speed approaches $c$, not mass itself, see: en.wikipedia.org/wiki/Mass_in_special_relativity. $\endgroup$ – Gert Nov 18 '15 at 15:11
  • $\begingroup$ yes, it is true. But I think it's just a matter of angle to consider this formula. I remembered that the way I used existed a long time ago. Now the common explanation is just what you said. $\endgroup$ – bitsoal Nov 18 '15 at 15:17
  • $\begingroup$ No, it's not a 'matter of angle'. You're contributing to the dissemination of a misconception. That should not stand on a forum about physics. $\endgroup$ – Gert Nov 18 '15 at 15:21
  • $\begingroup$ ......It is true that considering this problem in terms of momentum is favored right now. But it does not mean the way I described is absolutely wrong. $\endgroup$ – bitsoal Nov 18 '15 at 15:39
  • $\begingroup$ @Gert. To say "wrong" about relativistic mass is too dogmatic. It is possible to formulate relativity with that language (and indeed it was the usual language for decades), it's just that the language creates unnecessary confusion without adding anything essential so the modern approach does away with it and only talks about the invariant mass. I'm a strong proponent of the modern usage, but a combative approach is not a good way to bring people around. $\endgroup$ – dmckee Nov 18 '15 at 15:52

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