Indeed they do spin. I used to bring in an old mainframe hard drive without the cover so my comp sci. students could see the innards. You've heard of a "head crash"? That occurs when the read/write head, which is flying just barely over the cushion of air above the disk surface, makes contact and 'scores' the drive, gouging out the magnetic emulsion storing the data. Not pretty. But it is the dual motion of the head going in and out over the spinning disk surface that allows for random (quick) access, like an old record player where you set the needle down on a particular track. You may not have known how it works, but you certainly made use of this design when you played music.

One of my desktop computer's Western Digital drives spins at 10,000 rpms. 7200 is still quite normal though, and 5400 is often used in laptops that don't yet have an SSD.

BIAB 2024 Win Audiophile. Software: Studio One 6.5 Pro, Swam horns, Acoustica-7, Notion 6; Win 11 Home. Hardware: Intel i9, 32 Gb; Roland Integra-7, Presonus Studio 192, Presonus Faderport 8, Royer 121, Adam Sub8 & Neumann 120 monitors