Disk spinner gummed up, can't spin fast enough for the disk to be read

Recently bought a used Gamecube. It boots up fine and eventually gets to the menu screen displayed when there's no disk. I do have a disk in it that works fine on my old Gamecube, but it says "no disk" when I select "Game Play". If I open the lid and close it again the no disk becomes a question mark, before quickly reverting to no disk again. I can hear the disk spinning briefly before giving up when it decides that there's nothing in there. The spinner is quite noticeably stiffer than my old one, and my guess is that it just can't get up to speed. I'm not sure if its something mechanical broken or has just gotten gummed up inside, but if anyone has thoughts on how to clean/fix the optical drive spinner I would be really grateful!

Thanks!