Oh yeah, holding a spinning Discman you could notice the gyroscopic force; don't pivot it too fast or it'll precess beyond the suspension's compliance and scrape the edge of the disc!
And that was only spinning at 1x; later faster data drives were weirdly powerful. I had a little experience with a 24x drive in a laptop and you didn't dare move it while the disc was spinning. Thankfully they never went faster than that in portables; a 48x slimline would've been dangerous.
