Okay, in high school physics class, this was probably the thing I understood the least, the concepts of centrifugal and centripetal force. This has been bugging me. I always thought that centrifugal force was a center-fleeing force, so that when you spun on the merry-go-round, you would fly off, since you would leave the center. (This is because of inertia, right?) I was then told in school that there was actually no such thing as a centrifugal force, only a centripetal (center-seeking?) force, which doesn’t really make sense to me since you don’t get sucked into the middle of the merry-go-round. Anyway, I guess the point of this is that I have a very loose grasp on these concepts and it all seems jumbled and mish-mashed, so could some physics-minded Dopers help me to put it all together?
It depends on your frame of reference. Let’s say you are swinging around a ball on a string. If you look at it from the inertial frame (i.e. not rotating with the ball), the ball is continuously accelerating*, and the force that is causing the acceleration is centripetal force (i.e. the tension on the string). There is no other force needed to explain the behavior of the ball.
If you step into the rotating frame, the tension of the string is still there. But the ball is now stationary in this reference frame. Why? Because centrifugal force is pulling the ball in the opposite direction, balancing the centripetal force. The net force on the ball is zero in this particular reference frame.
Some take this to mean that centrifugal force is not a true force. This, IMHO, is misleading. It’s as real as any force, it just happens to be a force that depends on your choice of reference frame.
*Acceleration is rate of change of velocity, not speed. The speed of the ball may be constant but its direction is changing, so the ball is “accelerating.” You need a force to cause this acceleration.
It depends on your frame of reference. Let’s say you are swinging around a ball on a string. If you look at it from the inertial frame (i.e. not rotating with the ball), the ball is continuously accelerating*, and the force that is causing the acceleration is centripetal force (i.e. the tension on the string). There is no other force needed to explain the behavior of the ball.
If you step into the rotating frame, the tension of the string is still there. But the ball is now stationary in this reference frame. Why? Because centrifugal force is pulling the ball in the opposite direction, balancing the centripetal force. The net force on the ball is zero in this particular reference frame.
Some take this to mean that centrifugal force is not a true force. This, IMHO, is misleading. It’s as real as any force, it just happens to be a force that depends on your choice of reference frame.
*Acceleration is rate of change of velocity, not speed. The speed of the ball may be constant but its direction is changing, so the ball is “accelerating.” You need a force to cause this acceleration.
I was always told that inertia describes it best. Which is just swell, because most people understand what you mean when you say centrifugal force - the most frowned upon word between centripetal, centrifugal and inertia.
Your inertia is what would cause you to fly away from the center.
I think scr4’s explanation of reference frames is pretty good, if a little confusing. Before studying different reference frames, I had always been told “centrifugal force” was what you could call a “pseudo-force” because it was a result of the change in velocity and the inertia that is tending to keep the body moving in a straight line. When you ride the merry-go-round, true, it doesn’t “feel like you’re getting sucked into the middle,” but there has to be a force there keeping you moving in a circle, otherwise you’d just fly off because of your inertia. That force keeping you moving in the circle is the friction of your shoes and the floor surface.
Mathematically, when you sum the velocity vectors at different points along the circle of motion (assuming the rotation is at constant speed), the resultant vector will always point to the circle’s center. The magnitude of this acceleration will equal v[sup]2[/sup]/R, where v is the speed and R is the radius. The force a body feels will equal that acceleration times its mass. That’s where centripetal force is calculated.
I agree with what has been said here. It is the conventional wisdom, but don’t forces always come in pairs???
Likewise, I, too, have never fully understood why we appear to be forced to lean away from the center (when in a car going around a curve) instead of being pulled inward. A friend once put it as your body wants to keep moving forward, but the car is turning and your body (still moving in a straight line - now always tangent to the curve) runs into the side of the car. Seemingly, it feels as if you have been pushed outwards. Is this how other SDopers have been taught to picture it?
Even if this is a correct description, I fail to clearly see how one is under the influence of a center-seeking force. To this day, I have just come to accept it. The ball-on-a-rope example helps because I can picture the tension in the rope, but then another question comes to mind…there must be a reaction force to the tension in the rope, and hmm, would this reaction force actually be “pushing on a rope?” (Didn’t they teach us you don’t push on a rope?) - Jinx
No… The reaction force is in the opposite direction (still pulling on the rope/string) and acting on whatever is on the other end of the rope (spindle, your hand, whatever).
Wait a minute! Here’s another brain teaser! What about planets moving in an orbit? There’s no friction there, AND gravity pulls inward + centripetal force pulls inward, so why don’t the two forces add up as one big tug inwards? What keeps the planets in orbit? A-ha! You’d say centrifugal force, right? So, it is real, or not? Perhaps, it is an “observed” effect we mistakenly call a force? (But is that, more correctly, a reaction force???)
On a miniscule level, you might have to argue it out that the inertia of a planet keeps in moving in teeny-tiny straight line paths undergoing infintesimal, instantaneous changes as a star’s (i.e. the sun’s) gravity tugs at it as it goes around.
To go where no sane brain would dare to go… :eek:
- Jinx
Well, first off, I’m not a cosmologist. (“Dammit, Jinx, I’m an engineer, not a cosmologist!”) By definition, you can’t have centripetal force/acceleration without a body moving in a circular path. For a planet with a moon, or Space Shuttle orbiting Earth, the speed of its orbit has to be fast enough to balance the gravitational attraction. That speed is dependent on the distance from the center of the body and the gravitation acceleration of the body.
No, I’d say, “whatever got them started orbiting in the first place,” but then, not being an astrophysicist or cosmologist, I don’t know what those forces are.
Oh, ghod. Gravity IS the centripetal force acting on objects in orbit. On a merry-go-round, the centripetal force is the tension on the various parts. In a car, the centipetal force is friction from the car’s tires, directed by the steering mechanism, and transmitted by torque and tension on the axles, frame, and other components. The car’s passengers experience a centripetal force exerted by the car’s seats (friction) and other parts of the interior (tension, torque). Now, one might call the reaction force exerted on the car itself by its passengers “centrifugal force,” but it’s always smaller than the centripetal force if you view the situation from an inertial reference frame. (An inertial reference frame is one that’s not accelerating. A rotating frame of reference is, by definition, accelerating. Laws of motion are much more straightforward in an inertial reference frame.)
That’s what you have to argue on any level, because that’s what’s happening.
Not always, you’re trying to apply logic valid in non-accelerated frames into an accelerated frame. Moving in a circle is not a natural form of movement; nothing will move in that kind of way unless a force is forcing it to do so.
In order for an object to move in a circle, it must first have an initial velocity at first. Then there must be a central force that ‘pulls’ it in, the centripetal force. And, well, that’s all you need. If the initial velocity is high enough that it allows the object to maintain a steady orbit of sorts, then you have an object orbiting around a single point; no centrifugal force needed.
What you are feeling when your car goes around a curve is your body’s want to go forward, not a force pushing you outwards. So like Philster said, inertia is a better way to think about it rather than some sort of outward pushing force. The car is being accelerated by it’s wheels (centripetal force) in some sort of semi-circular orbit but your body still wants to go straight forward, so that’s why you feel pushed away from the center of the orbit.
If you replace the surface of the sun with an incredibly long flat pancake, stretching trillions of miles, then (ignoring for the moment any effects that would have other than the trajectory of the earth) the arc of the earth’s orbit would end with a thump after awhile, just like a baseball’s trajectory.
The reason the earth stays in orbit is indeed “inertia”, in the sense that until and unless air resistance (not a factor) or godzilla with a baseball glove (not a factor) or the surface of an incredibly long flat pancake act to slow it down or stop it, it’s going to keep on moving in a straight line.
The reaon the earth doesn’t fly away from the sun (or the pancake) is gravity, the same reason that a well-hit fly ball doesn’t continue to rise in a straight line from where the bat hit it, up over center field, up over the fence, up over the city, up through the clouds, out into space, etc. Gravity makes it arc, stop ascending, then start descending, all the while continuing the forward non-vertical part of its momentum until it thumps to the grass. Air resistance (in the case of the baseball) also slows it down some.
If you went to play baseball on a tiny little asteroid and caught the ball good and solid, the curve imparted to the baseball by gravity might be so gradual that it “misses” the surface of the asteroid – a quarter mile out yonder the land is not just “out there”, it has curved down and away from us, so the ball would have to fall a lot farther to get down to the ground. As it keeps falling it also keeps going “out there”, away from us, so the curvature of the asteroid’s surface keeps dropping the surface down out from under the falling baseball. Keep doing this and the next thing you know, zzoooom, what’s that overhead? The baseball, still falling, never falling fast enough to catch up to the curvature of the asteroid. Congratulations, you put a baseball in orbit.
As I wrote earlier, it depends on your frame of reference.
If you look at it from the inertial frame, the earty is constantly accelerating towards the sun because of centripetal force. In this case, centripetal force is provided by gravity. The earth doesn’t fly off into deep space because gravity keeps bending its path, confining it in a circular path.
If you look at it from the rotating frame (i.e. 1 rotation/year around the sun), the earth is stationary. The two forces acting on it, gravity and centrifugal force, are equal and in opposite directions. So they cancel out, and the earth doesn’t go anywhere.
Both viewpoints are equally correct.
The previous comment was: Don’t forces come in pairs?
This doesn’t make sense. All forces apply an acceleration (even if a negative value). Remember, F=ma? Ok, for circular motion, IIRC, there are two linear components which can be expressed as a tangential and radial component. Or, if you wish to show angular acceleration, you’d use Tau=I*alpha.
You’re thinking of a celestial body moving along in a striaght line that suddenly gets grabbed up by a gravitational field. But, what about a can sitting atop a record player when the turntable is initially at rest? It has no initial velocity, yet it will exhibit circular motion.
- Jinx
You can see scr4’s excellent explanation by simply applying Newton’s second law:
F = ma = mv[sup]2[/sup]/2
In the inertial frame the centripetal force on the left is balanced by the mass times the acceleration on the right.
But in the rotating frame there is no acceleration so you have an unbalanced equation
F[sub]centripetal[/sub] = 0
In order to rectify this you must add a second force to the left hand side of the equation
F[sub]centripetal[/sub] - F[sub]centrifugal[/sub] = 0
So in this respect a centrifugal force is most definitely a real force, but since it has no source it still has a little pseudo associated with it.
I have nothing to add to scr4’s explanation, other than a comment on the “reality” of pseudo- or fictitious forces. When viewed in the context of General Relativity, centrifugal force is exactly as real as is gravity. In the context of GR, a planet moving in an orbit has no net force on it, and is therefore moving along a geodesic (the closest approximation to a straight line, in a curved space). It is not accelerating. You can consistently say that it has no forces at all acting on it, or that it has two fictitious forces acting on it, gravity and centrifugal force, which cancel each other out, or you can call both of those forces “real” (whatever that means). Any of these three explanations is equally valid. But it is not valid to say that the gravitational force is “real” but the centrifugal force isn’t.
Except that Newton’s Laws only hold true in inertial reference frames. If you choose a rotating reference frame you choose a non-inertial frame and Newton’s Laws don’t apply. Ring’s application of Newton’s 2nd law is incorrect and there is no such thing as the centrifugal force.
In terms of classical Newtonian physics if a body is rotating it will experience a force directed towards the center of its rotation. This force is known as the centripital force. In most of our real world experience the centripital force is caused by something on the outside of the circle. For example the centripital force in that amusement park ride where you spin around is caused by the wall of the ride. The term centrifugal force comes from the fact that the human body only detects forces imparted to it. What I mean is that if I have a rod and I push the rod into you it will feel no different than you pushing yourself into the rod. It feels the same becuase in both cases there is an action/reaction force. In the first case we feel the “action” force of the rod pushing into us. In the second case we feel the “reaction” force of the rod as we push ourselfs into the rod. In the case of the ride the wall is applying a force to you but that feels the same is if you are applying a force. Our experience tells us that we are applying a force to the wall becuase almost all forces we experience are action/reaction. We term the “force” that we feel we are applying to the wall as the centrifugal force but that classification is incorrect.
I think the reason that most have trouble grasping this concept is that they think of acceleration as a change in speed. In the case of uniform circular motion your speed remains constant but your direction changes. The reason your direction changes is due to the centripital force. If there were such a thing as the centrifugal force the two forces would cancel each other and you would keep moving in the same direction. In the case of the ride this means you would go flying off.
Believe it or not Jinx you just thought up of what we term Calculus.
It feels as if you are pushed outwards becuase you feel the force that the wall imparts on you. The way the human body works is that you don’t feel forces you impart on objects you feel the force they impart on you. In other words you don’t feel yourself pushing against the door you feel the door pushing against you. If you had a friend push on you against the wall you would feel the same type of force as in going around the turn becuase the door is imparting a force on you in both cases. However in the case of the turn you aren’t applying a force on the door.
It’s embarrassing to say the exact same thing a previous poster said, but I swear scr4’s second (non duplicate) post was not there when I hit submit.
Just to expand on this a bit here’s what another guy wrote:
Let’s say I place myself (well-dressed in appropriate astronaut attire) and one of those Olympic hammer-throw thingies out in the interstellar space between clusters of galaxies, a handful of hundreds of billions of light years from any stars but surrounded, if you look out far enough, by the mass of the universe. And I proceed to spin like a skater.
We can “hold me motionless” and consider the relative motion to consist of the universe spinning around me as its axis, or we can consider me to be spinning (as I initially described it), but I’m pretty sure the hammer-throw thingie is going to extent itself as far from my center of mass as it can get, tugging my arm along with it.
You’re saying we can conceive of the hammer-throw device as stationary, in which case the force acting against the inward tug of my arm is this thing called “centrifugal force”, but in order to define the hammer-throw as stationary, I have to define the rest of the world as orbiting around me as I orbit around the hammer-throw device, yes?
Somewhere in there somehow is a concern about the velocity of very distant objects and a formula pertaining to radial velocity and linear velocity and radius and so forth, a thing that continues to make relativity smell more suspect when applied to rotational motion instead of linear motion…probably something that was explained in Physics the day I stayed home sick…
::smack::
uhh, hundreds of millions. Not billions, just millions.