I understand that in order for an object to maintain circular motion, its velocity vector must be travelling perpendicular to its position vector and constantly changing inwards, hence an acceleration towards the center of the circle. I know that the acceleration towards the center is typically caused by other forces, like tension on a string, and that these are called centripetal forces I believe? However, objects in circular motion tend to want to be away from the center instead of towards. A bucket of water tied to a string and twirled around in a circle will result in the water staying in the bucket: if the water is exhibiting circular motion, would it not thusly be accelerating inward, and thus escaping the bucket? I’ve heard that it’s a difference of frame of reference, but even looking from out to in, I can’t see how the water would be accelerating inward and yet remain in the bucket without support. Would there not be some force pushing the water into the bucket? And yet, centrifugal force is considered a fictitious force. I don’t understand. I know I understand some level of physics but please explain it like I’m 5 because I can’t seem to actually understand this.
‘Fictious force’ is a poorly phrased term.
Its more like an emergent, or secondary force, as opposed to a fundamental or primary force.
It isn’t ‘fictitious’, as in, wholly not real, its more like ‘contingent’… these rules well describe many realistic and common scenarios and their behavior, but they’re not perfectly universal, they require common, but not strictly universally present conditions.
I like this video about it (from Sixty Symbols), which gives a good simple overview with visual to help understand:
https://www.youtube.com/watch?v=cPEwkMHRjZU
The first half of the video focuses on centrifugal vs centripetal force
Some others have said some good things, but I’ll add a few more comments:
Objects will continue moving in the same direction at constant velocity unless acted upon by an outside force. In the circular motion case, as you correctly state, the velocity vector is always perpendicular to the acceleration vector, which does point inwards towards the center of the circle. The object IS accelerating inwards – the water in the bucket in your example is accelerating inwards. It’s just that it is also already moving tangential to the circle and the result of the inwards acceleration is the object turning to follow the circular trajectory. It’s distance from the center remains constant instead of increasing.
This is all the ideas of centripetal acceleration from a stationary frame of reference outside of the water-bucket system. There is no extra centripetal force. In your water-bucket example, there is a force the bucket applies against the water to give the water its centripetal acceleration. Some people call this a centripetal force, but I don’t like that phrasing, because it sounds like its an extra force. A water-filled bucket sitting on the ground also exerts a force upwards on the bucket. We typically call this a normal force, so in the spinning example, the normal force of the bucket against the water is causing the water to move in a circle. Likewise, the string tied to the bucket - the string is exerting an inwards tension force on the bucket that causes the bucket to travel in a circle, and thus have centripetal acceleration. If you cut the string, the bucket stops turning and instead goes in the straight path in the direction of its velocity vector.
Now, think of the fictitious centrifugal force as from the frame of reference of someone moving in the circle. I like to use the example of you sitting in a school bus with those slick plastic-leather seats as the bus goes around a turn. You “feel” like you’re being pushed outwards. In actuality, there is insufficient frictional force to keep you turning in the same circle as the bus, so you are traveling in the straight line that your velocity vector is pointing. Thus you “feel” like you are being pushed outwards. The term centrifugal force arises because that “feel” can be modeled mathematically from the perspective of the rotating object, and we call it a centrifugal force. This term is mathematically equivalent to the centripetal acceleration term from the previous stationary frame of reference.
Imagine slamming on the gas in your car. The car lurches forward, pushing your seat into you, and you start to accelerate forward.
As the driver, though, you feel like you are being pushed back into your seat, though it’s pretty obvious that there is no force pushing you back, it’s just the inertia of your body trying to stay put.
The only force in that system is the force of the car accelerating you forward, and the feeling of being pushed backwards is a fictitious force.
It’s the exact same with rotational motion, just trickier to wrap your head around. If you have acceleration, you know there are unbalanced forces, and an object in orbit is constantly accelerating.
This.
Ficticious force doesn’t mean that it doesn’t act like a force. From the frame of reference of the car, it totally liiks like there’s a force pushing you into the car seat, and as a passenger in the car, there’s no way to judge from the acceleration alone whether the car accelerated or the Earth’s gravity field changed.
Or to put it differently: it feels identical to stand in a space ship accelerating upward at 1G and standing in the same space ship while it’s parked on the surface of Earth.
Think of the inertia of a bucket of water on a string that you are holding by the string.
If you are standing still the water and bucket and string behave like you expect.
Start running suddenly and the bucket will seem to swing back behind you. Your frame of reference is in motion. But when I watch you do this I see a bucket and water at rest. Their inertia resists the sudden acceleration.
As you pull the string along in your run, the swinging will stop. And with no acceleration (you are in a constant running velocity) the bucket will hang straight down again. The bucket and water are in your moving frame of reference. Their inertia is clear.
What if you stop?
Just like when you started running the inertia of the bucket and water will cause them to continue moving, swinging up. Their inertia is linear, but show up as an arc due to the string you’re holding when you accelerate to a stop. The water stays in the bucket because it’s geometry tilts its axis, keeping the bottom pointing in the direction of the watet’s inertia.
If you were carrying the water on a spoon in the same conditions the water would spill. Because it doesn’t tilt the right way to hold it in.
If, at that moment of stopping, you started swinging your arm in a circle you could create a circling bucket from your question. Sometimes the bucket will be upside down, but with sufficient acceleration the water will stay in.
It’s the inertia doing the trick. Aided by the geometry of the bucket.
The water stays in the bucket because its geometry tilts its axis, keeping the bottom pointing in the direction of the water’s inertia
I was with you until this line. I spent some time thinking on it and I think I sort of get what you were talking about? Let me see if I can’t explain it back to you. The water and the bucket both want to keep going linearly, which they can’t because of the string. The bucket arcs around, but the inertia of the water keeps going linearly, causing it to press against the bottom of the bucket. If the bucket continues to be driven in circular motion, it’s this momentum that drives the water against the bottom of the bucket? While the side of the bucket drives the water along the circular path?
Right - the water has inertia in a straight line (as does the bucket). When they both try to go straight the string prevents it, accelerating them in a new direction. At each moment you look at the circular path the water’s inertia wants to go in a straight line (tangent to the circle). So at each instant it is behaving exactly as if you had been running in a straight line and stopped.
What I meant about the geometry and axial tilt - imagine that instead of a bucket you had a dinner plate with a bucket handle. So the water was all at the level of the top of the bucket rim on a plate. As soon as you stopped the plate would flip and the water would splash off. Likewise, if you had the string connected only to the bottom edges of the bucket rather than its handle, as soon as you stopped the bucket would flip due to the water’s strong inertial force against the side of the bucket. The setup doesn’t tilt the bucket in the right way to keep the water contained and impart the new acceleration upon it.
Like you said, objects in a circular motion want to be away from the center of a circle instead of towards it. Centrifugal force is the term to describe that specifically. It’s a “made up” force, because there is no force pushing an object away from the circle.
Q: How is there no force pushing an object away from the circle?
A: An object moving in a circular motion is at all times already trying to move away from the circle. If you take the bucket of water for example, and suddenly deleted the bucket, the water would keep flying in the straight line it was trying to go in. The direction it would fly would be sideways, perpendicular to a line drawn to the center of the circle and not outward away from the center.
Q: Is the water accelerating inward?
A: Yes! The bucket pushes the water keeping it from going in a straight line. Likewise, the string pulls the bucket which keeps the bucket from flying out. And you are spending the energy to cause the force that is being applied to the string. This is known as “centripetal force”. It’s the force that makes the circle going objects change direction.
Q: If there is force or acceleration inward, why doesn’t the water fly towards the center?
A: Acceleration is not a change in speed. It is a change in velocity, which is a combination of speed AND/OR direction. So the water doesn’t fly inward because centripetal force only causes a change in direction (the bottom of the bucket keeps the water from going straight). If someone punched the bottom of the bucket while it was swinging in a circle, then the water would fly inward out of the bucket because that would cause a change in speed toward the bucket.
Short summary: Nothing is pushing the water into the bucket, the bucket is pushing the water so it continues to accelerate in a circle. The water wants to go straight. That is inertia.
Your third point clarifies some things for me a lot. I seem to have forgotten that acceleration describes a change in direction and/or a change in magnitude of the velocity vector: I recall now in my physics textbooks that objects in non-constant circular motion have a tangential acceleration, and the total acceleration lies somewhere between those, but if the velocity remains constant, then the only acceleration is the centripetal acceleration describing the change in the velocity’s direction.
However, I still have some questions about points one and two. I understand that things in circular motion want to fly out tangentially away from the center, not radially away. Yet, in so far as I can observe, objects do seem to press outwards radially. In the example with the bucket of water, the water sticks to the bottom of the bucket instead of pressing against the side wall. In another example, that of those carnival rides that spin people around in a saucer (gravitron I think it’s called?), the carmival goers tend to stick to the wall of the ride as though they were being flung out radially, instead of rolling along the edge or something else. I guess it’s this disconnect between what I know is correct (objects fly tangentially to their circular paths) and what I observe (objects stick to the wall radially away from the center).
That’s fair. The reason it seems to stick to the bottom is because it is the bottom of the bucket causing the change in direction. Kinda confusing right?
There is an outward force, as the bottom of the bucket pushes the water to have it change direction, the water does push on the bucket in the opposite direction (3rd law). But, this is not a “centrifugal force” which describes a force pushing the water outward. To reword, the water is making a force against the bucket in response to the bucket’s force on the water, but that force is soley generated by and in response to that interaction. Ironically, this might be easier to visualize with a satellite in orbit and gravity. Gravity is pulling the object toward Earth, that’s easy to understand. But, the object is also moving laterally around Earth, so it sorta is kinda in a state of constantly falling (centripetal force) and missing. Same with the water, but it’s the bucket pushing and not gravity pulling.
This might raise the question: Why does the bucket need walls to keep the water in?
First, to get the bucket in motion, starting from rest, you do need to increase and maintain it’s speed, and same with the water in it, that force is a different force to the centripetal force (though in this case the same source being your arm). On the gravitron the force to speed you up is friction which exists due to the normal force caused by the centripetal force itself. And in space it’d be like booster engines or smthn idk. Second, there is air in the way on Earth.
I hope that helps.
Thank you for this explanation.
Two sentences that are a bit confusing:
The direction it would fly would be sideways, perpendicular to a line drawn to the center of the circle and not outward away from the center.
fly inward out of the bucket because that would cause a change in speed toward the bucket
The blue line that says velocity is the way the water will travel if you delete the bucket. Newtons first law.
Centrifugal force implies that the object wants to move away from the center of rotation, which is false.
The object wants to continue forward, tangentially to its current rotational moment of inertia (I hope I’m using those terms correctly). If the centripetal forces are released (think of throwing a shot put), the object does not fly straight out from center, but 90 degrees from the last moment it was held in rotation.
It’s called a fictitious force because there’s not actually a universal phenomenon like gravity or electromagnetism that causes it. When the bucket starts moving, the water is at rest, and the bucket’s motion causes the water to move in a single direction. When the bucket’s vector starts to change, the water’s vector does not. The water is still moving in the original direction, but that direction is now “outwards” from the centre, and the bucket exhibits new motion on the water, changing the direction it’s traveling again. The water is trying to escape the bucket, but in the direction it’s already going (outwards), not towards the centre of the circle the bucket is tracing. Remove the bucket, and the water goes flying off away from the center of the circle.
Another way to understand a fictitious force is to think of a bunch of marbles in a box, packed tight so all the marbles are touching and none of them can move. Each marble is a particle, push on one and you affect others around it. Now, remove a marble so you have a space, and only one marble can move at a time. And now, reverse your vision - the space left by removing the marble is the particle, an “anti-particle”, and the marbles are free space. Push on the marbles, and the anti-particle moves around like a marble would. It’s not a marble of course, it’s a space, so you could call this “anti-particle” you just created “fictitious”.
So it’s not that the water in the bucket is accelerating inwards, because it’s not the water maintaining that circular motion at all - it’s the bucket maintaining the circular motion. The water’s “inwards acceleration” that keeps it moving in a circle is actually just the water’s inertia, relative to the motion of the bucket.
Let me see if I understand this. So the bucket acts on the water, pushing it in a direction, then the bucket’s motion changes, changing the motion of the water, then this repeats ad naseum in a circle. So the bucket is experiencing a centripetal force (tension from the string), but not the water: it’s motion is changing as a result of the bucket pushing on it. So then if the bucket is moving in a counter clockwise direction, the “left” wall of the bucket would be the thing acting on the water. Wouldn’t that cause the water to stick to the left wall of the bucket, not the bottom?
In regards to your example with the marbles and anti-particles, I understand it in principle, but I’m not quite sure I get how fictitious anti particles relate to fictitious forces. I mean, I think I get it, and I understand what you mean by it not having a universal phenomenon driving the force. I’m just not sure I could explain it back to you.
So then if the bucket is moving in a counter clockwise direction, the “left” wall of the bucket would be the thing acting on the water. Wouldn’t that cause the water to stick to the left wall of the bucket, not the bottom?
It might help to remember that “left” and “bottom” are different depending on where you’re standing. The water keeps moving in the direction the original force got it moving, but as the bucket traces the circular path, the “left” and “bottom” walls are now in different positions relative to the water. Remember, you don’t see the water sitting peacefully on the “bottom” of the bucket like you would if it were standing at rest; the water is forced in the “bottom left corner” of the bucket while it spins, because the water always being accelerated (by the bucket) tangent to the direction its already moving.
Also, the bucket is absolutely experiencing the force of the water acting on it - right from the start of the string pulling taut, the water has been pushing on the bucket’s walls (and even before, actually, the whole time the water is in the bucket). But that’s not really relevant.
I’m not quite sure I get how fictitious anti particles relate to fictitious forces.
Sorry, I didn’t mean to muddy the water - I was just trying to illustrate why it’s called “fictitious”. It looks and acts like a force (or a particle, in the case of the marble), but it isn’t one because it doesn’t actually exist outside that frame of reference. Centripetal force is the “pull” towards the centre of the circle that is required for circular motion; if you think of the actual motion of swinging a bucket around on a string, you’ll be pulling on the string (if you don’t pull, the bucket flies off in a straight line, along with the water in it). And, if you don’t pull the string, and the bucket and water fly off in a straight line, then the water (and bucket) no longer experience the centrifugal force they got while tracing the circular path.
I recommend you look at some physics resources, perhaps even YouTube videos, searching beyond the AI-generated summary that your web search gives. You wrote almost word for word what google serves back as AI summary for a “centripetal vs centrifugal” search. Look further. Plenty of science educators have posted high-quality lessons for those who seek them out.
Don’t give up when the AI summary doesn’t make sense. Effective websearching is still a modern critical skill despite AI summaries, heck, even more so because of AI summaries.
No offense but please don’t insult me like this. I abhor AI and the whole reason I ask this is because I’ve been reading through my old physics text book and got to the part with circular motion. I’ve watched the crash course video on circular motion and have read through physics forums explaining this and the Wikipedia article for this subject and I still don’t understand it.
I understand where you’re coming from and I know you don’t know me, so it’s a fair assumption considering how much fucking AI there is, and I appreciate you encouraging actual research instead of consulting AI, but damn do I feel insulted.
