system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How does shifting work? Without it grinding and making horrible noises.

I imagine there’s some sort of flywheel or some kind of mechanical terminology. But when I’m driving downhill, I sometimes put it in neutral, only to shift back into drive when back on level ground. 
(I know, probably unsafe too. In my mind, I’m saving $$$)
But when I make that shift, isn’t something going from 0rpm, and being engaged to something going 1000+rpm? Shouldn’t it make a horrible noise?
gpt
You are not saving money, btw. If you're going downhill, your vehicle's momentum will spin the wheels, which in turn spins the axles, differential, transmission, and finally spins the engine. If you put the transmission in neutral, the wheels can't turn the engine anymore, so the engine will need to consume fuel to maintain idle.

When you shift, there are clutches that gradually match things that are rotating at different speeds. Non-CVT automatics have friction bands and clutch packs, manual transmissions have synchronizers.