m98 -- the problem is analogous to the physics riddle of: "how long does it take for a ball to fall down an incline with friction coefficient a. zero (frictionless), and b. 1.0?"

In the first case, the ball does not rotate, and the answer is simply the physics of a mass on an incline. In the second, the ball rotates; its inertia is coupled to its mass by friction, and the answer is (for a uniform ball I think) 40% more or something like that.

The mass equivalent of rotating parts is not very much in a typical vehicle, though, so I don't know to what end the OP needs this.

Also, regarding the link, I'll note that the transmission was omitted, and the engine and transmission are complicated by shifting anyway. Better to ignore them both; they are turned into heat dissipated during shifting (equivalent to switching loss in an electrical circuit).

Both would need to be included, in a dynamics problem where the transmission is locked in a given gear and the vehicle is accelerated some way.

In any case, that's simply how it's calculated, it's straightforward. You get the moment of inertia, link it to mass via gear and wheel ratios, and there you are. Just ratios and addition. You need to know the moment somehow or another, which if you know the geometry of the elements, it can be calculated roughly; else it can be measured, or perhaps looked up in a catalog/datasheet.

On a more fanciful note, there is

*real* mass gain, on the order of micrograms, due to the energy stored in the rotating masses and Special Relativity. There is also a frame-dragging effect of those masses on nearby space (General Relativity). Both are essentially impossible to measure when materials lighter than neutronium are involved.

Tim