# Mass, Momentum, and Velocity: Exploring the Dynamics of Change

• mike232
In summary, mass changes as you approach the speed of light, but that mass is more accurately termed "relativistic mass". Momentum increases differently depending on whether you think of mass as energy or as rest mass.

#### mike232

Hey guys,
I'm reading my modern physics book over break and I remember hearing that mass changes as you approach the speed of light. But is it really the mass that is changing or just the amount of momentum a certain mass can have. So is mass really varying or is it the energy capacity of mass that is changing with respect to velocity?

mike232 said:
I remember hearing that mass changes as you approach the speed of light.

The "mass" that changes as your speed changes is more precisely termed "relativistic mass"; but that term is not used much in modern physics texts because it is just a synonym for "energy".

mike232 said:
is mass really varying or is it the energy capacity of mass that is changing with respect to velocity?

I'm not sure what you mean by "mass really varying" as opposed to just "energy capacity of mass" changing; if "mass" means "relativistic mass", then "mass" and "energy" are just different names for the same thing (see above).

OTOH, if "mass" means "rest mass", or better, "invariant mass", then it is an inherent property of the object and does not change as the object changes speed.

So by defining mass as simply confenced energy... I'm thinking of p=ymu. So because the variant mass is mass times 'demensionless velocity' the momentum increases differently than classic, the classic idea of mass changed but the rest mass, intrinsic energy of matter, doesn't change?

mike232 said:
by defining mass as simply confenced energy

Relativistic mass is the same as energy (not sure what you mean by "confenced"). Invariant mass is not. It's important to keep this in mind because the term "mass" and the symbol m won't always be explicitly defined as one or the other, you have to look at the context. See below.

mike232 said:
I'm thinking of p=ymu.

In this formula, m is invariant mass, not relativistic mass. So m in this formula is not the same as energy.

mike232 said:
because the variant mass is mass times 'demensionless velocity' the momentum increases differently than classic,

The momentum increases with velocity differently from the "classic" case (I assume by "classic" you mean "Newtonian") because of the factor ##\gamma##; you don't have to think of "variant mass" (by which I assume you mean "relativistic mass"--it really helps to keep your terminology consistent) at all.

mike232 said:
the classic idea of mass changed but the rest mass, intrinsic energy of matter, doesn't change?

What do you mean by "the classic idea of mass"?

As for rest mass, I'm not sure it is best thought of as "intrinsic energy of matter", because, as I noted above, invariant mass is not the same as energy.

It might help if you gave a specific quote from your book, or a specific example of a scenario you're not sure about.