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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> By definition, a spinning object is under acceleration… And force requires energy, so why doesn’t the spinning of an object expend its angular momentum and slow it down over time?
Force does not require energy.
Forces do work on something (or objects do work against a force) when the thing moves **in the direction of** (or away from) **the force**.
If you slide something across your desk the force of gravity is pulling that thing down, but you aren’t doing any work against gravity because the weight is pulling the object down, while you are moving it sideways.
The key thing about (stable) circular motion is that while everything is being accelerated inwards, it is only moving in the circular direction, so no work is done by or against the force; the motion is always at right angles.
With non-circular angular motion (so ellipses etc.) work is done by and against the force, but it cancels out; as the thing gets closer to the centre of rotation work is done by the force on the object – it gains energy (usually speeding up). But as it moves back away work is done against the force – it loses energy (usually slowing down).
Does that help with your questions?
If not, feel free to ask for more details.
Eeeh though one to explain but let’s try.
A spinning object doesn’t accelerate as long as no forces are applied and the inertia stays the same. The acceleration you are mentioning is only there when changing the height relative to the center of rotation. Which doesn’t happen on the earth or in a coin.
However
Imagine an figure skater spinning with wide arms. The moment their arms come closer to the center of rotation. The rotation will speed up. Once widening the arms again. The rotation slows back down. This happens because of the energy staying roughly the same, but the moment of enertia decreases and increases again (how hard it is to rotate the object). But no energy has been lost doing so.
Force doesn’t require energy. If it did, anything in a gravitational field would eventually collapse because it ran out of energy to withstand the field.
>And force requires energy
Nope. This is where you’re going wrong and getting confused. A stone can sit on the surface of the earth for decades without requiring any energy input, yet it has an upwards contact force from the ground that’s balancing its weight, keeping it in place.
What requires energy is exerting a force over some distance – i.e. pushing that stone along against friction, or lifting it up against gravity. More specifically, force in the direction parallel to the motion. In circular motion, the force is perpendicular to the direction of motion, so it does not require any energy exertion, and hence things can keep spinning indefinitely if there’s no frictional force or something else slowing them down.
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.)
Your premise is wrong. A spinning object is NOT under acceleration by definition which is why the angular momentum is not consumed.
Force doesn’t “require” energy necessarily. A force perpendicular to the direction of motion does no work. If you want to be precise, work done is the integral of the dot product between the force vector and the infinitesimal change of position.
So if you push something in the direction it’s moving, you give it kinetic energy. If you push something against its motion, you take it’s kinetic energy. And, with a rotating object, when the force (the centripetal force) is perpendicular to the motion (the rotation), no work is done.
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