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Can flags flap around on the moon due to lack of air? Yes they can due to lack of air resistance! This is very basic Physics taught correctly in most schools, but not all.
Paper & feathers etc will fall at the same speed as a hammer or even a chunk of concrete in a vacuum. Air slow objects down; including flags. As the flag continued to sway on the moon, it becomes proof that they were in a vacuum.
A heavy washing line on the moon could flap to and fro for days due to lack of air resistance to halt the motion. Illustrations by Brian Van de Peer