Por que o RPM de uma hélice de passo fixo muda com o passo de uma aeronave?

The driving variable here is airspeed, not pitch attitude per se. Your airplane naturally goes faster when you put the stick forward and decrease the wing's angle-of-attack, and this changes the prop rpm.

Your pitch input is changing the wing's angle-of-attack which leads to an airspeed change. Even with the engine switched off, the aircraft would fly (glide) at a higher airspeed with the stick forward than with the stick aft. And for a given throttle position, a fixed-pitch prop turns faster at a high airspeed than at a low airspeed.

Just as a wind turbine does.

Your tachometer can be used as an airspeed indicator.

The key factor is the speed of the air flowing through the propeller disk-- with a fixed-pitch prop, this dwarfs any effect related to the amount of air being forced into the engine.

And yes, this effect can be explained in terms of the angle-of-attack of the propeller blades. Increasing the airspeed decreases the angle-of-attack of the propeller blades, "unloading" them, or in extreme cases subjecting them to negative loading so that the prop is driving the motor rather than vice versa.

In a fast dive at a low power setting, the wind (airflow) is making the prop move, not the other way around, and you'd pick up more airspeed if the prop fell off. But even at a lower airspeed and higher power setting, the speed of the oncoming airflow has big influence on the speed of the prop's rotation.

Because airspeed influences the effective angle of attack of your propeller blades.

Consider what happens when you move this propeller from a stable cruise condition to a dive. In a dive, the incoming airstream increases, so a propeller with a fixed geometric pitch will have a smaller eficaz angle of attack. It will then generate less lift and drag, and thus need less torque to rotate.

Consider this paint.exe marvel:

An increasing forward speed component tends to align the airflow with the propeller blade, reducing its angle of attack.

Since the rpm of the propeller-engine combination is stabilized where the torque output of the engine equals the torque requirement of the propeller, the rpm will increase to the new equilibrium.

Because your hydrostatic load mudado

The RPM changed instantly because the hydrostatic load on your prop changed. Because air is a fluid. Effectively, your prop is a fluid coupling.

An example of "not a fluid" is an engine geared to cogs on a rack railway. An RPM change must match a speed change. Not here.

Compare to your car's automatic transmission torque converter- the most common fluid coupling in normal life. It intentionally has "slip" so the engine can idle at 600 rpm while the car is stopped. This slip varies by engine force: if you push the accelerator, the engine will rev amoras while still stopped. On a slight downhill, it slips less, and on a steep downhill, it can actually push (windmill??) the engine*.

There is a relationship between throttle position, engine RPM, and hydrostatic load (resistance).

Your propeller is the engine side of a torque converter.

When you pitch down, you change induced drag, i.e. the airflow is resisting menos. You have instantly removed hydrostatic load from the prop, so the engine RPM instantly increases.

Put it another way, at any given altitude, weight, pitch and throttle position, the airplane will seek to "balance out" at a particular RPM and airspeed. But it won't get there instantly. You can change pitch angle very quickly, but it takes awhile for airspeed to change.

So in that moment when you have pitched down and you have not gained airspeed, the air is resisting less (because the airplane wants to go downward on its own, like going down a hill on a bike)... so the RPM devo aumentar.

Again, air is not a rack railway.

* however you can't "windmill" start an automatic transmission car. That's because the gears are engaged hydraulically by a pump on the engine side...