Changing mass with velocity

Question

I was wondering that a change in velocity can change the mass of an object slightly. I thought of this since p=mv so if we rearrange it to be m=p/v. Does this mean that a change in momentum or velocity can actually change the mass?

user277610 · Accepted Answer

You have this equation, $p = mv$. If you increase the velocity and keep $p$ constant, yes you must have had an increase in mass. The question is, what does it mean for $p$ to be constant? It is defined by the product of mass and velocity. So you have done nothing to make predictions, you have just stated what you would call mass if you increased v and kept p the same. OR since mass and velocity are more readily known as measured quantities to the layman, you have said increasing v and lowering m keeps mv the same. See? you've said nothing of any value

Correct answer by user277610 on June 4, 2021

JEB · Answer

Note, for a small change in $p$ (and $v$, as their correlation is 1, or $m$ depending on normalization):
$$ delta m = frac d {dp}({frac p v})delta p+ frac d {dv}({frac p v})delta v $$
$$ delta m = frac{delta p} v - frac{pdelta v}{v^2}$$
Since:
$$ delta p = m delta v$$
we get:
$$ delta m = frac{delta p} v - frac{pdelta p/m}{v^2}$$
$$ delta m = delta p(frac 1 v - frac{v}{v^2})$$
$$ delta m = delta p(frac 1 v - frac{1}{v}) = 0$$
So, no.

Changing mass with velocity

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