I bet you learned in school that momentum is mass times velocity - I sure did!
However, for objects moving close to the speed of light, like the particles in the Large
Hadron Collider or light itself, this equation is no longer accurate.
Instead, we use these equations that I talked about in more detail in the video "E=mc^2
If you take them as your starting points and solve for momentum, you'll find that objects
with mass have momentum equal to their mass times velocity, DIVIDED by the square root
of one minus velocity squared over the speed of light squared.
That square root part doesn't make much difference if your velocity is small compared to the
speed of light, because then v over c is really small and 1 minus something small is basically
just 1, so momentum (p) is pretty much just mv divided by 1, which is mv, which is why
you learned in school that momentum is mass times velocity.
That's also what physicists thought before 1905, but now they know that's not quite true…
and so do you!