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Does relativistic mass phenomena only appear while accelerating or even when the object is travelling at constant velocity (say 90% speed of light)?

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    $\begingroup$ Can you explain what you mean by "relative mass phenomena"? $\endgroup$ – probably_someone Jun 14 at 13:08
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    $\begingroup$ Briefly, it only depends on the velocity, not how you reach that velocity. Modern treatments of relativity avoid the concept of relativistic mass because it can be confusing and misleading. See physics.stackexchange.com/q/133376 $\endgroup$ – PM 2Ring Jun 14 at 13:09
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    $\begingroup$ To add to @PM2Ring's comment, relativistic mass is literally just another name for the total energy of a particle. $\endgroup$ – probably_someone Jun 14 at 15:42
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The formula for relative mass is $$ M_r = \frac{M_0}{\sqrt{(1 - v^2 / c^2)}}. $$ where $$ \begin{align} M_r &= \text{relativistic mass}\\ M_0 &= \text{rest mass}\\ v &= \text{velocity}\\ c &= \text{speed of light} \end{align} $$ So the relative mass is affected only by the speed.

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    $\begingroup$ True, but friends don't let friends use relativistic mass. ;) BTW, you can use the MathJax dialect of $\LaTeX$ here, eg $m_r=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ $\endgroup$ – PM 2Ring Jun 14 at 14:31
  • $\begingroup$ I tried to google that real quick, but didn't that it was MathJax, thanks. I will edit it now. Edit: someone beat me too it. $\endgroup$ – Dr_Bunsen Jun 14 at 14:33
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    $\begingroup$ It's not called relative mass, it's called relativistic mass. $\endgroup$ – Ben Crowell Jun 14 at 17:55
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    $\begingroup$ @jacob1729 I agree with Kyle that we should discourage the use of relativistic mass, but I wouldn't downvote an answer that uses it in response to a question like this that directly asks about relativistic mass (assuming the answer is technically correct). However, I do expect such answers to at least mention that relativistic mass is a deprecated concept. $\endgroup$ – PM 2Ring Jun 17 at 10:14
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    $\begingroup$ @Dr_Bunsen basically any SR textbook made after the 1950s. Surely any modern treatment (say last 20 years). $\endgroup$ – Kyle Kanos Jun 18 at 11:42

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