Well, first of all I don't use rotating disk on a drill to sand through grits. I did when I started but didn't like the clouds of dust or what it sometimes did to the wood. I have no problem with those who power sand as long as I'm elsewhere!
There ways that work better for
me, even with larger bowls and platters. If I do use disks for platters and such, it is usually 600 grit on a small pneumatic ROS running at a very low speed.
Since I do most sanding by hand, I keep sandpaper on a long dispenser rod on the wall when I can reach it without moving. It has grits from 400 and coarser.
The dispenser has 1" and 2" wide rolls of Klingspor Gold. I just tear off a piece when needed.
I know this won't work for everyone but works for me and everything I turn.
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I put 1"x3" strips of finer grits - 600, 800, etc - in the little tilt-out bins below the rolls along with small pieces of cloth, fine steel wool, etc.
Since I use the coarsest grits for brake drums and such, I removed one set to make room for paper towels. (I cut a big roll into narrow rolls - then I can tear of just a small piece to apply finish, clean up glue, etc. I can't remember who I stole that idea from - he cut slices of rolls using the bandsaw but I didn't like the chewed up edges so I always cut them with a sharp fillet knife.
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As always, much depends on what you turn and how you work.
JKJ