How Much Faster Does a Ball on a String Spin When You Pull It In? A Mate’s Physics Lesson
Alright, mate, let’s have a yarn about this ball-on-a-string business you brought up. You’ve got this image in your head: a ball whizzing around on a bit of cord, you yank the string shorter, and it spins faster—like some carnival trick. You’re wondering how much faster it goes, and you’ve tossed me two options: does it jump to 1200 rpm or a wild 12,000 rpm? I’ve been mulling it over with a bit of physics and some back-of-the-envelope scribbles, so let’s crack into it like we’re chatting over a couple of brews at the pub.
Picture this: you’ve got a tennis ball tied to a meter-long string, and you’re swinging it around your head like a lasso—say, at 60 rpm, nice and steady. That’s one spin a second, nothing too crazy. Now, you pull the string in so it’s only half a meter long. What happens? The ball doesn’t just keep trucking at the same pace—it speeds up, and it’s all down to this thing called angular momentum. It’s a fancy way of saying that spinning stuff likes to keep its “oomph” constant unless you muck with it. When you shorten the string, the ball’s got less room to roam—it’s circling a smaller radius—so it spins faster to balance the books.
Here’s the guts of it: in physics, angular momentum is mass times velocity times radius, and it stays the same unless you add extra force—like a big tug or friction slowing it down. If we ignore air and all that jazz for a sec (keep it simple), the key bit is that when you halve the radius, the rotational speed—those spins per minute—doubles to keep that momentum steady. So, if you’re at 60 rpm with a one-meter string, pull it to half a meter, and bam, you’re at 120 rpm. It’s not about the ball magically hitting some set speed like 1200 or 12,000 rpm—it depends on where you started and how much you shorten it.
Now, your options—1200 rpm or 12,000 rpm—sound like you’re testing me with some wild guesses, so let’s ground it. Say your ball’s already spinning at 600 rpm (10 spins a second, pretty brisk). Halve the string, and it’d jump to 1200 rpm. That’s plausible if you’re swinging it hard to begin with—like a kid with a yo-yo on steroids. But 12,000 rpm? Mate, that’s 200 spins a second! You’d need to start at 6000 rpm and then halve it, and even then, you’re in helicopter-blade territory—strings snapping, balls flying, chaos. A typical setup—like something you’d muck around with in the backyard—doesn’t hit those numbers. Think more along the lines of doubling from, say, 100 rpm to 200 rpm, or 600 to 1200 if you’re really giving it a go.
Why doesn’t it just rocket to 12,000? Real life’s messier than the textbook. Air drags it down, the string’s got tension limits, and your arm’s not a machine. Plus, rpm—revolutions per minute—isn’t fixed; it’s tied to how fast it was going and how tight you pull. The rule’s called conservation of angular momentum—shorten the radius, speed shoots up inversely. Halve the distance, double the spins; quarter it, quadruple it. I saw some lads online spinning stuff at 300 rpm, yanking it in, and hitting 600—nothing near 12,000 unless you’ve got a motor involved.
So, between your two picks, 1200 rpm’s the winner if we assume a decent starting point—like 600 rpm—then pulling in the string. It’s a realistic jump for a “typical” ball on a string, something you could test without breaking the laws of physics or your arm. 12,000 rpm? That’s a pipe dream unless you’re secretly a cyborg with a steel cable. Want to give it a whirl yourself? Grab a ball, tie it up, and spin it—see if you can feel that kick when you reel it in. Bet you’ll clock something closer to 1200 than 12 grand. What do you reckon—up for a backyard experiment next weekend?
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