Why is centrifugal force “false” and centripetal force “real?”
Centripetal force is the force required to keep an object moving in a circle. It can come from gravity, or from a string or a rope, or it can be exerted by a circular wall on the outside, or any number of other places, but it’s the very real force needed to make an object that wants to move in a straight line instead follow a circular course.
Centrifugal Force is a “fictitious Force” because it’s an artifact of a mistaken image of reality that assumes you are in an inertial reference frame when you are, in fact, in a non-inertial frame, generally a rotating one. You seem to feel a force pushing against you throwing you away from the center of rotation. What it really is, of course, is the centripetal force from the first example pushing against you force=ing you into that curved path, but your mind tends to assume that you’re in the inertial frame of reference, so that force you feel must be coming from somewhere else.
You can obtain the magnitude of fictitious forces by vector subtraction of the motion of your frame of reference – it’s not all centrifugal. There’s also Coriolis Force and, if the frame is accelerating uniformly along one direction as well, there a fictitious force associated with that, as well.
Obligatory XKCD comic: http://xkcd.com/123/
Fuck, that’s a good reply*, but I’ll braindump here anyway…
Think about how you describe motion in Newtonian terms. You add up all the forces acting on a body, to get the total force. Then you use F=ma to work out the acceration, and thence the movement. But hidden behind all this, is the big question, movement relative to what? But don’t worry, we don’t need to bring Einstein into all this just yet, Newton is perfectly good for now. And let’s talk about linear motion before going on to circular motion.
Imagine a cannonball starting at rest, and dropped from… hmm, where do cannonballs like to be dropped from, oh yes, the Leaning Tower of Pisa. Let’s consider its motion with respect to the Earth’s surface. It accelerates. Downward. At 9.8m/s^2. Because of gravity. Gravity is a quite real force.
But now, consider its motion, and for good measure, the motion of everything else in the universe, with respect to the cannonball itself. Well, obviously enough, its motion with respect to itself is… nothing. It’s at rest relative to itself. But, how on Earth (ha ha) can it be at rest when there’s a force of gravity on it? It seems that if we ask its motion with respect to the Earth we can use Newton’s Laws, but if we ask its motion relative to itself, we can’t! It gets even worse… what’s the motion of everything else in the universe relative to the cannonball? Well everything else is accelerating UPWARDS at 9.8m/s^2. Which means that, if we’re a sentient cannonball trying to apply Newtonian mechanics, it appears there must be some force upwards, acting to produce the same acceleration on everything except, bizarrely, ourselves.
How we get out of this is indeed to say that, within the reference frame of the cannonball, there are indeed upward forces acting on everything. These are ‘fictitious forces’ because they have no real physical origin, such as gravitation or electricity, or friction or air resistance. These fictitious forces must be proportional to each body’s mass, so that the accelerations are all the same. And the fictitious force acting upwards on the cannonball precisely cancels the real gravitational force downwards, hence meaning the cannonball experiences no net force, and hence no acceleration, in its own frame.
So now let’s swing a cricket ball round in a sling. In the reference frame of the person doing the swinging, the cricket ball moves in a circle. Hence it is accelerating. If moving at constant speed (let’s arrange it like that), the acceleration of the ball is directed straight towards the person at the centre of the circle. Hence that’s where the force is pointing (hence, ‘centripetal’). And it’s a real force, it’s caused by the tension in the sling.
But from the point of view of the cricket ball, it’s at rest. But it can’t be at rest, when there’s a force pulling it towards the person, UNLESS there’s an opposite force pushing it away. That opposite force is ‘centrifugal’, and it’s fictitious, because it appears only due to the fact that we are measuring motion relative to something that is accelerating (the cricket ball).
God I hope that made sense.
Excellent responses so far.
I’ll just add another example or two. If you are in the passenger seat of a car making a turn to the left, you feel a force that appears to be pushing you to the right into the car door. However, this so-called centrifugal force is fictitious. It only appears in your reference frame inside the car.
From an inertial reference frame outside the car, it is apparent that the door of the car is pushing you to the left in a curved path. This real force (a force that the car door exerts on you to the left) is a centripetal force. You, of course, are simply trying to keep going in a straight line. If the car door were to open suddenly, you’d keep going in a straight line as you tumbled out of the car.
The same thing is true when you swing a ball around on a string. From an inertial point of view, the string exerts an inward centripetal force on the ball. If you let go of the string, the ball continues on in a straight line. While swinging the ball around, the only force that was actually being exerted on the ball was an inward force.
I used to teach this material some years ago as a physics teacher. I used to spend quite a bit of time spinning a ball on a string around as a visual prop.
Both explanations are awesome - in particular Nancarrow opened for me a different line of thought - imagining the forces one would need to construct on the assumption that I (as a cannonball) am at rest.
When explaining this to my grade schooler, I would lose her with words like “inertia” and “frame of reference” (not to mention vector subtraction 
).
So I say to her: Imagine we’re riding in a car. You’re in the back seat, no seatbelt. The bench is really slippery. I suddenly swerve left which makes you suddenly slide right. What’s pulling you? Well, nothing - the car is changing direction but you’re not yet. You’re trying to keep going straight while the car is moving underneath you. But it sure feels like something is pulling you. That feeling is an illusion - a fictitious force.
Good explanations so far, so I won’t try to add my own. But I’d like to add one point of clarification, because I know it’s something that confused me when I first learned about fictitious forces.
The term “fictitious forces” doesn’t really mean that the forces are wrong or false or imaginary. If you’re driving around a corner in a car, and mention that the centrifugal forces are pushing you to the side, and some pedant sitting next to you says, “no, you’re wrong, there’s no such thing as centrifugal forces – they’re fictitious!” you have my permission to slap the pedant.
Fictitious forces are forces that arise when we determine the equations of motion in a non-inertial reference frame. As long as we’re working within the same reference frame, they describe the motion of objects in just the same way as other, “real” forces. Is there any rule that says that all physics must be conducted in an inertial reference frame? No, there is not. And in many situations, it is far more convenient to work in a non-inertial frame.
One classic example of this is the description of motion on the surface of the earth. If you are aiming artillery, you will probably find it far more convenient to calculate the Coriolis force within your non-inertial reference frame than calculate the projectile’s motion in an inertial frame. The same is true in meteorology, for describing the motion of air masses.
Incidentally, it’s not my intention to suggest that anyone in this thread has suggested that fictitious forces are off-limits. It’s a misconception that I picked up from an early physics teacher, which confused me for some time. So I thought I’d post to help prevent this confusion in others.
And tell them it is a d’Alembert force.
To further strengthen the point made by the browned protein duck, it should be pointed out that, according to General Relativity, gravity has the exact same status as centrifugal or other “fictitious” forces. If you want to call gravity a “real” force, whatever that means, then consistency forces you to also acknowledge centrifugal force as “real”.
Here’s one guy’s opinion
No offense intended but definitionally this sounds like the pedantic answer. 
Yeah, you’re probably right. But sometimes you’ve got to fight pedantry with pedantry!
I want someone to change their name to Sentient Cannonball (or a new user to take it…it’s awesome!)
I’m 3/4 of the way through a Mechanical Engineering degree, I’ve had a depressing number of physics/mechanics courses that have covered the math and some explanations of what is happening, and I’ve managed to piece together what is happening enough to do the work, but I have never had explanations as clear as the ones in this thread. I love coming here and being able to reinforce what I’m learning through fantastic posts like the ones in this thread.
I also owe the Dope for providing the first explanation of complex/imaginary numbers as rotation operators I’ve ever seen…after spending a couple of years using the damn things to solve problems.
I think I might have crappy profs.
I once had a physics professor friend. Somehow, a question of one or the other came up. He made a quick discourse, and then, actually started laughing about how anybody could have ever thought that there was such a thing as centrifugal force!
I am frightened by this kind of thinking.
Best wishes,
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