Is it safe to drive remote control cars on carpet?

Yeah it's fine. Eventually you'll have to pull off the wheels and get the carpet fibers that are wrapped around the axle and the motor drive shaft out but that's not a big deal.
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Yes, it is alright to drive an R/C car carpet floors, just make sure the carpet isn't too long to get tied into the wheels. its a pain in the butt to get the carpet out of the wheels or unwrapped from the drive shaft because it is wrapped so tight
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Its safe to run remote control cars on carpet, you should be careful of the type of the carpet because if it is shag or another long carpet there are chances that it will get wrapped up on the wheels. If it is an expensive carpeting cars with studded wheels are possibly not the best thing because when they are sliding around they can cause small snags, its nothing serious for normal high traffic carpet but something like carpet in your office where it is designed more for decoration than actually being walked over repeatedly with high traffic will suffer more. Short answer is normal short carpeting you can play with almost any type of car, shag or longer carpet taller cars with more lift is better, smooth carpeting something with harder racing or normal car wheels will do fine.
Don't stress too much and have fun with your son, maybe you can get a car and the 2 of you can race them
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I have had dozens of RC cars when I was younger, and had different types of carpeting in my house.

Its safe as long as the battery does not overheat or the battery pack does not leak…….
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