I understand why it needs to exist, otherwise the Earth wouldn’t keep spinning, coins would fall over immediately when you tried spinning them, artificial gravity wouldn’t be possible, etc. But I’m not sure how it works out physically. (nb. I’m talking without regard to drag, friction, etc. For example out in space where those are negligible factors.)
By definition, a spinning object is under acceleration (individual points on the object are constantly turning around the center of rotation, which is a form of acceleration in linear physics). And force requires energy, so why doesn’t the spinning of an object expend its angular momentum and slow it down over time?
Along the same vein, how does artificial gravity work in this context? As I understand it, centrifugal force is a fictitious force, but if I am inside a spinning object I am still being pressed against it as it turns and subjected to acceleration (from an observer’s point of view, at least). And so since I am being accelerated, something has to be using energy to accelerate me, right?
I apologize if I am sounding stupid but this has been wracking my brain for the last while and I’m desperate to figure out the answer. Thank you for any help!
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The laws of physics are counterintuitive because we never witness them in their “raw form” on Earth. In particular, Newton’s First Law, which states that an object at rest will remain at rest, and an object in motion will remain in motion, unless acted upon by a (net) force.
The problem is, on Earth there are always forces. Gravity is constantly pulling everything down. That in turn means most things touch the ground or some other surface, and therefore experience friction with that surface when you try to move them. And even if they aren’t, then they’ll be surrounded by air or water, both of which provide friction too.
As a result, anyone born into this world with no prior knowledge will pretty soon conclude that there is a general law of physics that says that anything that moves will, with time, always slow down and come to a stop, unless you apply some force to keep it moving. In other words, at first glance all the evidence point to the exact opposite of Newton’s First Law.
It takes careful observation and experimentation to discover the true law, and even then you never see it in its purest form. You can create a near-vacuum and levitate something in a magnetic field, and still the forces on the object will not be exactly 0. But, it will be near enough to observe that when you start your floating object spinning, it will keep going for a very long time, as the remaining forces that slow it down are infinitesimally small.
Still, you can know at an intellectual level that Newton’s First Law is true, but to accept it intuitively is another matter, because it so completely disagrees with your daily experience. Things tend to slow down, always. They just do.
If this is true for you, then I’m not sure I can change that with a few lines of text, because really all I can say is: they don’t. Newton was, in fact, right.
Perhaps it helps if you ask yourself the question: *why* would things always need to slow down? Why, when there is nothing pushing back, would a spaceship stop moving? Why, when there is no friction, would a ball in space stop spinning? It’s much easier to explain why things would not stop moving *unless* something makes them.
As for your question about artificial gravity: first, consider that regular gravity also continuously pulls down on you. However, as long as there is an opposing force (from, say, the ground you stand on), you don’t actually experience a net acceleration, and there is no work being done. No energy being transformed. It’s only when an object falls under gravity that gravitational potential energy gets converted to kinetic energy. There is no paradox there; no energy you get from free out of nowhere. After all, you can’t harvest unlimited energy this way. Once the object has fallen to the ground, it stops. If you want it to fall again, you need to lift it up first, which means you have to supply the energy that will be converted to potential energy.
Artificial gravity from centrifugal motion is similar. Within the rotating reference frame of, say, the spinning spacecraft that you’re in, you aren’t being accelerated. Therefore, there is no energy being converted. You don’t gain any energy from the centrifugal force, and no energy is lost from the spinning spacecraft by your being inside it. (Things can get a little complicated if you start moving inside the spacecraft, especially you move closer to or away from the center of rotation. Angular momentum (and energy) will be conserved, but due to the shifting masses, the rotation will speed up or slow down.)
(In short, these last two paragraphs can be summarized as others ITT have put it: forces do not require energy.)
(You might say, but hang on: what if we examine the system from a non-spinning, inertial frame of reference? (I don’t know if you are the sort of person who would say such a thing, but just in case…) In that case, yes, you are constantly being accelerated, but from that perspective, you are constantly converting your own kinetic energy into kinetic energy that’s pointed in a different direction. At any given instant, you have a linear velocity tangent to the circular motion that you are experiencing over time, and the magnitude of this velocity (your speed) will be the same always, and therefore your kinetic energy will be the same as well. So again, energy is conserved. And (if you were wondering) the constant redirecting of linear motion (which is more simply described as rotational motion) is being done by the centripetal force which is orthogonal to your linear motion tangent to the circle. Indeed, it is these two things, your own inertia and the centripetal force, that give rise to the fictitious centrifugal force.)
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