A fidget spinner illustrates this for me--bear with me. When I spin it and it just stays at rest in my hand, it spins fast. But when I quickly move my hand carrying the spinner, you can see it slows down the spin rate, and then when I stop moving it, it speeds back up. While the mechanisms are entirely different (classical vs. relativistic) they both show motion can affect certain fundamental properties of a system, whether it be spin rate or the passage of time
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