Hi, i am having trouble understanding why centrifugal force is a “psuedo” force. Centripetal force holds an object in rotation pulling toward the centre , whereas centrifugal force is pushing the object outwards.
I have veen trying to watch videos but the examples dont really help.
For example, if im in a car going around a corner, the faster i go, the more the car wants to fly off the road.
Or if an object us on a spinning platform like a lazy susan, the faster i spin the lazy susan, the further away the object gets (until it falls off).
Is centrifugal force just the lack of centripetal force?
In: 5
**td;dr**:
A centripetal force is whatever combination of forces is needed to get something to move in a circle; we have to push or pull it inwards.
A centrifugal force is a mathematical tool we use if we want to look at things from the perspective of whatever is turning. We take the centripetal acceleration (we must accelerate inwards to go around in a circle) and move it to the other side of our key equation (F = ma), turning it into a negative (so outwards) force.
Neither thing is strictly speaking a force. The first is a mass x centripetal acceleration, the second is a mathematical trick to treat an inwards acceleration as an outwards force, when switching perspectives.
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So, to talk about this we need to get into reference frames. This is going to be a deep dive.
In physics, when we look at something, we need to decide on a perspective we are looking at things from. The most obvious choice is where our co-ordinate axes go; where are we taking to be the origin? What are we taking to be “velocity = 0?” But also things like “where are we taking our zero potential energy level to be?”
This will depend on context, but no matter which reference frame we pick we should be able to get the same results or – at least – results that are consistent. We should be able to switch between reference frames and get consistent results.
This is the notion of *relativity*.
What we observe is not absolutely objective, but is *relative*; it depends on the reference frame we look at it from, but in a predictable, objective way.
It turns out a key thing that matters with relativity (Galilean, Special or General) is *acceleration*. If two reference frames are only different by some constant velocity (their “velocity = 0” things are just different by a constant) then things look pretty much the same but for that difference in velocity. But if there is some acceleration going on between those reference frames (one is accelerating relative to the other) then things start to get a bit messy. Acceleration matters because our core equation in this kind of physics is Newton2: **F** = m**a**. Forces tell you about acceleration. Acceleration is supposed to be an absolute thing and link to all the forces. So if your reference frame is accelerating this equation won’t quite work; you will be missing some of the acceleration.
An example! You throw a ball up in the air and catch it. We want to understand how this will work, how the ball will move.
What reference frame should we take?
The easiest one is your perspective. We take you to be at rest, we take the ball to start at the origin, and we get a neat constant acceleration (ignoring air resistance) problem.
But maybe you’re sitting at a table on a train moving at some constant velocity **v**. We could switch to a reference frame where the ground is at rest, the train is moving. If we try to model the motion of the ball we get pretty much the same answers – the acceleration is the same – but we have to add on a **v** to the ball’s velocity, and therefore (with a bit of maths) a **v**t + **c** to the ball’s position with the **c** being where the ball starts relative to our new origin).
But what if the train was speeding up or slowing down? You might have experience this; everything feels a bit weird; things seem to start to move on their own, you feel pushed back into your seat or lifted off it. You are now trying to work in an *accelerating* reference frame, and that messes with our calculations. We need to improve our model to account for that.
Of course that train is on the Earth, and the Earth is spinning through space – which is a form of acceleration. So even if we are sitting still on the ground we are in an accelerating reference frame, so we might need to factor that into our model.
It probably isn’t noticeable to us with our ball, but going back to our first reference frame, if we want to model it more precise we need to add some extra terms to our equations to account for the fact that our entire reference frame (us sitting on the train) is accelerating. And this is where we get “Coriolis” or “Eötvös” effects. If our train is moving Eastward around the Earth our ball will appear to be a bit lighter than it should be (because the Earth is falling away below it); if we are moving Westward our ball will appear a bit heavier (because the Earth is spinning up to meet it).
Now, note what I said there; the ball *appears to be lighter*. The ball isn’t any lighter. The ball spends more time in the air when we throw it because, due to the Earth spinning and us moving around it, the Earth is curving away from the ball. But we, sitting on the train, don’t notice that, because the Earth is also curving away for us. From our perspective the ball is lighter. We have an effect (the ball stays in the air for longer) but we have a different cause of that effect depending on our perspective because we are moving between accelerating reference frames. Objectively the ball isn’t lighter, but it appears to be lighter from our perspective.
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Now let’s talk about centripetal v centrifugal forces.
> if I’m in a car going around a corner, the faster I go, the more the car wants to fly off the road.
The car wants to go straight. General rule in physics (Newton1) things want to keep doing what they’re doing. Things moving want to keep moving in a straight line at a constant speed unless you mess with them.
To get a car to go around a corner it has to accelerate; it’s velocity (which covers both how fast it is going and in which direction) has to change – the direction it is moving has to keep changing inwards. If we do a bit of geometry we find out that this acceleration must be pointing towards the centre of the circle we’re going around, and have a magnitude of v^(2)/r where v is how fast we are going and r is how far we are from the centre of the circle. If we go twice as fast we need 4 times the acceleration to keep us going in a circle.
We also have Newton2: **F** = m**a**
For something to accelerate there must be some overall force in that direction. In the case of our car this will be the friction between our tyres and the road (ish). If we’re going too fast that friction won’t be big enough to meet our acceleration requirements, it won’t be enough to pull us around in a circle, and our car goes flying off the road. Note that we can get some help by having a banked road (old race tracks often have [these giant curved banks](https://i0.wp.com/heritagecalling.com/wp-content/uploads/2017/07/brooklands-historic-photo-copyright-brooklands-museum-surrey.jpg) for the corners) we can get a bit of extra inwards force from the road pushing us in.
So… from a reference frame standing by the road we see our car experience an overall inwards force and that accelerates it inwards; **centripetal** acceleration (centri + petal, petal is Latin, to do with seeking or heading towards). The car is being pulled inwards.
But what if we look at it things from inside the car? We *feel* pushed towards the outside, not pulled inwards. But that’s because we want to go forwards, and the car (our reference frame) is accelerating inwards. Like our ball on a train earlier, because our reference frame is accelerating we *feel* like we get an extra force. There is nothing physically pushing us outwards, there is no “real” force. But we feel one because everything around us is accelerating inwards. We feel a **centrifugal** force because we are in an accelerating reference frame. But remembering relativity, this perspective is perfectly valid. There is nothing wrong with being in an accelerating reference frame, we just get some slightly weird results, like forces that aren’t really there. They are the corrections we have to make to our model to account for the acceleration.
If you want to look at the maths, let’s go back to Newton2:
> **F** = m**a**
where **F** represents all the random forces acting on our thing, and **a** tells us the corresponding acceleration. From outside the car we get:
> Friction etc. = m x centripetal acceleration = m v^(2)/r
So our “Friction etc.” is our centripetal force note that centripetal force isn’t strictly speaking a physical force caused by something either – it is the combination of different forces that cause our centripetal acceleration. The distinction is kind of subtle but quite important. It is a mass x a centripetal acceleration, not strictly a physical force.
Looking at us, sitting in the car, as the car goes around the corner we will be “pushed” up against the outside car door; there will be some reaction force (from the door, our seatbelts etc.) pulling or pushing us inwards. Taking inwards to be our positive direction, and looking at it from the outside, we get:
> Seatbelt force = mass x centripetal acceleration
> R = m v^(2)/r
(where this m is now *our* mass, not the car’s mass).
But what if we look at this from a reference frame inside the car? We are sitting still in the car, not accelerating, so we need the right hand side of F = ma to be 0. We feel that push/pull from the seatbelt holding us in place, but also that centrifugal force pulling us outwards. What we’ve done is moved some terms around in our Newton2 equation:
> F = ma
> R – m v^(2)/r = 0
In order to “pretend” we are not accelerating we have moved the acceleration to the other side of our equation, turning that inwards acceleration (which was on the right of F = ma) into an *outwards* force (the minus sign meaning it has changed direction).
That “-mv^(2)/r” is our **centrifugal** force (fugal comes from Latin to do with running away).
Like our ball that seemed lighter than it should be, we’ve included a correction to our forces to account for the fact that our reference frame is accelerating. We don’t think we’re accelerating because everything around us is also accelerating, and we process that by adding in negative (outwards) force.
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