Some of the science books I have read use the concept of relativistic mass and some don’t. All of the books that do use this concept define as it as m[sub]0[/sub]*gamma, where m[sub]0[/sub] = the rest mass and gamma = 1/(1–v[sup]2[/sup]/c[sup]2[/sup])[sup]1/2[/sup]
However I have since learned that there are actually two relativistic masses, the longitudinal relativistic mass and the transverse relativistic mass. Where m[sub]RL[/sub] = gamma[sup]3[/sup]m[sub]0[/sub] and m[sub]RT[/sub] = gammam[sub]0[/sub].
Ok, I got it. If you define force as dp/dt instead of m*a and demand that momentum be conserved then the need for longitudinal mass disappears.
The original requirement for longitudinal/transverse mass was due to having both length contraction and time dilation in the direction of motion, but only time dilation perpendicular to the motion.