Shammy / Chamois
1/2 inch diameter wood dowel (Wood is a good call if you're cleaning glass. An aluminum dowel could work, but just be careful not to crack your glass carboys)
There are many potential improvements to be made. This is a nice quick 10 minute project: low effort with high payout -- one of the best coefficients to be had.
Step 1: Use a Shammy / Chamois
Cut your shammy into a disc about 30cm in diameter.