I am a university educated (primarily sciences), middle aged dude and I still cannot understand the difference between these 2 forces / phenomena.
In: Physics
tl;dr: a centri*petal* force is the total force required to make something travel in a circle or curve, and points *towards* the centre of the curve.
The centri*fugal* force is a fictional force used when trying to model something in a situation where it and everything around it is going in a circle. Rather than treating its whole universe as accelerating inwards, we pretend there is some force pushing it outwards, and the maths all works out.
The centripetal force is what is going on when viewed from the outside. The centrifugal force is what you “feel” when on the inside.
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In more detail…
We have Newton’s 2nd Law, often written as *F = ma*.
This tells us that the *total* force on an object is equal to its acceleration, scaled by its mass. This has a few key consequences:
1. if something is accelerating, there must be some overall force acting on it,
2. if something isn’t accelerating (even if moving at some constant velocity), there must be no overall force acting on it (all the forces must be balanced),
3. if something has some overall force acting on it, it must be accelerating, and
4. if something has no overall force acting on it, it must be stay at the same velocity (kind of Newton’s First Law, ish).
We’re mostly going to be dealing with 1 here.
For something to be going in a circle, or curve, it must be accelerating. Acceleration is rate of change of velocity, velocity has a direction. If something is curving it is changing direction, so its velocity must be changing, so it must be accelerating, so there must be some overall force acting on it.
With a bit of geometry, that force must be pointing inwards, and we can work out its magnitude in terms of the speed and radius of curvature.
This is our centri*petal* force. It isn’t strictly speaking a force, but a *sum of forces* – it is the overall or total force needed to make our thing go in a circle (i.e. it is really the right-hand side of *F = ma*, a mass multiplied be a centripetal acceleration, not any one force on the left-hand side). “-petal” in this context comes from the Latin word for “seeking” or “aiming at”, (where we get words like compete, perpetual, repeat). If something is going in a circle the “centripetal force” tells you what overall force must be acting on that thing.
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But that’s not what *we* feel if we are the object moving in a circle. If you’ve ever been in a car going around a corner too fast, you *feel* pushed to the outside, not pulled inwards. What is happening in that case is that you are trying to keep going forwards (Newton’s First Law), but your local “universe” (the car you are in) is accelerating inwards (to go around the corner). Because your local universe is accelerating inwards, and you are trying to go straight, within your local universe you seem to be pushed outwards.
The centri*fugal* force is this outwards push (“-fug-” being Latin for fleeing away from something). But it isn’t entirely real; nothing is actually pushing you outwards. You are really being pushed inwards (by the car). You only appear to be being pushed outwards because the universe you are in is accelerating inwards. So a centrifugal force is a way of modelling the fact that something is in an accelerating reference frame. Mathematically, what we do is take our Newton’s 2nd law:
> total F = m[centripetal acceleration]
and split off the bit of accelerating that our reference frame is doing (so going around in a circle), and move it to the other side:
> F – m[centripetal acceleration] = 0
And because of the maths the sign (so direction) changes. Rather than saying “we are accelerating inwards with our whole universe” we pretend we are being pushed outwards.
It turns out this can be really useful in some situations. We end up with a “fictional” or “pseudo-” force which is a correction to account for the fact that our entire co-ordinate system is accelerating.
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