# Physics/relativity question: Is centrifugal force "magic"? **URL:** \ **Category:** Factual Questions\ **Created:** [January 9, 2009, 2:15pm UTC](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522 "2009-01-09T14:15:40Z")\ **Posts on this page:** 5\ **Page:** 4
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [January 13, 2009, 9:17pm UTC](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522/61 "2009-01-13T21:17:12Z")
Quoth **tim314** : > [@](#): > > If I did the math right, I get a constant acceleration due to gravity of 2 pi G times the mass per area of the sheet. > > – > > You can treat the sheet as concentric rings around the point directly below you. Consider a ring of mass with radius R and mass dM = 2 pi sigma R dR (where sigma is the mass per area). A perfectly valid calculation, but it’s much simpler to do it using Gauss’s Law, which works just the same way as it does for electrostatics. Really, the only place to do that integral is in a textbook or class where you’re illustrating that Gauss’s Law works. As for the question of which frame is easier to work in, the rotating frame will always work, if you include the centrifugal and Coriolis forces, but for many problems, once the Coriolis force becomes significant, it’s easier to work in the inertial frame. If speeds are low enough for the Coriolis force to be negligible, though, the co-rotating frame is usually easier, and likewise if there’s a whole bunch of other interesting stuff that’s tied to the co-rotating frame. For instance, when discussing the weather, we don’t care where a hurricane is relative to some inertial reference frame, but we might care where it is relative to Florida. As an aside, those discussing objects flying and/or falling in rotating space stations might be interested to know that the current arc of the webcomic [Schlock](http://www.schlockmercenary.com/d/20081220.html) [Mercenary](http://www.schlockmercenary.com/d/20090112.html) deals with exactly such a situation. ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [January 13, 2009, 9:28pm UTC](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522/62 "2009-01-13T21:28:06Z")
If it’s helpful to anyone, [here’s a list](http://en.wikipedia.org/wiki/Rotating_reference_frame#Newton.27s_second_law_in_the_two_frames) of the extra “fictitious” force components that a mass experiences as observed from a rotating reference frame. If the rotation speed is constant, or close enough, then we can ignore the third component, the “Euler force”. The centrifugal force on a mass always acts directly away from the axis — “downward”, to those on the spinning space station — and is proportional to the distance away from it. The Coriolis force is a little trickier. It acts in a direction perpendicular to both the rotational axis and a mass’s velocity vector. In the simple case of a ball dropped from a short height, the Coriolis force means that the ball will land slightly “anti-spinward” from where you’d otherwise expect it to. For a jogger jogging around the station, he or she will experience the force as pushing him downward or lifting him upward a little, depending on whether he’s jogging with or against the spin. > [@hobscrk777](#): > > Isn’t it best to work out of an inertial frame, since things can get quite complicated in non-inertial frames. […] My understanding is that for more complicated scenarios, trying to apply classical mechanics to a non-inertial frame would case all kinds of havoc. Right, although since we _live_ on a rotating object, sometimes you have to choose which complications you’re happier with: fictitious forces, or switching reference frames. ---
**Author:** ![Bad\_Astronaut](https://avatars.discourse-cdn.com/v4/letter/b/e19adc/32.png) [@Bad\_Astronaut](https://boards.straightdope.com/u/Bad_Astronaut)\ **Post date:** [January 13, 2009, 11:30pm UTC](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522/63 "2009-01-13T23:30:02Z")
If you are interested in an expert opinion, Columbia physicist Brian Greene discusses the Newton’s Bucket/Weights on a String problem at length in his book “The Fabric of the Cosmos”. My understanding is it’s considered a fairly open problem. The behaviour of the spinning weights on a string in an otherwise empty universe has implications for the physical existence of space as an entity, rather than just an absence of anything. ---
**Author:** ![The\_Seventh\_Deadly\_Finn](https://avatars.discourse-cdn.com/v4/letter/t/6bbea6/32.png) [@The\_Seventh\_Deadly\_Finn](https://boards.straightdope.com/u/The_Seventh_Deadly_Finn)\ **Post date:** [January 14, 2009, 1:14am UTC](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522/64 "2009-01-14T01:14:41Z")
> [@Chronos](#): > > Even if the universe you popped out into _was_ empty, it’s not any more. When you started your ship spinning, you gave it angular momentum, which means that you also had to give something else an equal and opposite angular momentum. Maybe you spun a flywheel the other way, in which case your ship is now rotating relative to that flywheel. Or maybe you started your ship spinning by firing up your rocket motor, in which case you’re now rotating relative to your rocket fumes. No matter how you did it, you’re going to end up with something else in the universe which is not rotating the same way as you. Ouch. This has the ring of truth. Way to take all the magic out of it, Captain Buzzkill. 😉 So really the answer is that the net angular momentum of a closed system (even the whole universe) is always zero, and you’re always spinning (only) in relation to whatever you pushed off against in the first place. So that should obviate the necessity of Newton’s “absolute space,” right? ---
**Author:** ![The\_Seventh\_Deadly\_Finn](https://avatars.discourse-cdn.com/v4/letter/t/6bbea6/32.png) [@The\_Seventh\_Deadly\_Finn](https://boards.straightdope.com/u/The_Seventh_Deadly_Finn)\ **Post date:** [January 14, 2009, 6:37am UTC](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522/65 "2009-01-14T06:37:02Z")
I think I did it again with the too-sketchy-for-others-to-understand version of my argument. And now I don’t think anyone’s even listening any more. But oh well: Asking what would happen if you spun the weights in an empty universe is a meaningless question. How are you going to set them spinning? You can posit a magical force that sets something in motion without Newton’s “equal and opposite reaction,” but such a force doesn’t exist. In the real world, every action has an equal and opposite reaction. It’s part of the deal, and a thought experiment that ignores this won’t yield useful conjectures. If you accelerate your weights, there’s got to be, as Chronos points out, something physical that’s going the opposite direction-- a flywheel, or exhaust gas, or what have you. So while you won’t see centrifugal forces in an empty universe, and you do in our “full” universe, it’s not because all the other matter in our universe creates a magical matrix of reference to measure the spin against. (Which is what I thought in my OP.) It’s just because the original acceleration had to come from two masses heading in opposite directions, even if that momentum originated in a forgotten stellar explosion two billion years ago. The spin is measured relative to that original motion, whatever it was. You can’t make energy out of nothing. All motion is relative to its equal and opposite reaction. That’s the answer, I think, boring as it is. I wanted spooky action at a distance! [Previous page](https://boards.straightdope.com/t/physics-relativity-question-is-centrifugal-force-magic/480522.md?page=3)