More Centrifugal Force

[SeanF]

Came across this on the Snopes web site, a legend about Dead Man's Curve.

In about the middle of the second paragraph of the Origins section, it reads (in part):

. . . a long downhill stretch . . . leads up to the curve, where a driver suddenly finds he must bank sharply left or centrifugal force will send his car crashing through a wall of trees . . .

Dang that "centrifugal force" making that car keep going in a straight line!

[GrapesOfWrath]

I don't have a problem with centrifugal force--neither, apparently, do Misner, Thorne and Wheeler, in their tome Gravitation--but I'm a little confused about the snopes explanation. They keep talking about Hollywood and Vine being in the song, but that is not in their quoted lyrics. Is it just the other place names, or what?

Oops, that's not astronomy, is it? SeanF and I and anyone else interested in the lives of the stars will discuss this in email. (hey, wait a minute...)

[ljbrs]

I find it interesting to look in physics dictionaries and fail to find *centrifugal force* listed in most. If it is listed at all, it is called a *fictitious force* which is equivalent to inertia. It is not a *force* at all, because *inertia* is a *lack of a force*!

ljbrs [img]/phpBB/images/smiles/icon_lol.gif[/img]

[GrapesOfWrath]

The ones I like list gravity as a fictitious force.

[NottyImp]

Somebody I used to know used to insist that there was no such thing as "centrifugal" force, only "centripetal" force. I had no idea what they meant then, and I still don't.

I always thought Newton's first law covered the situation pretty well myself.

[amstrad]

On 2001-11-15 04:50, NottyImp wrote:
Somebody I used to know used to insist that there was no such thing as "centrifugal" force, only "centripetal" force. I had no idea what they meant then, and I still don't.

I always thought Newton's first law covered the situation pretty well myself.

If you have a bucket of water on a rope and you swing it in circles over your head, the water of course stays in the bucket. So what keeps the water in the bucket? Many people would say "cetrifugal force", but this is not correct. Like you said, Newton's first law explains it all. Inertia keeps the water in the bucket, and inertia is not a force. In fact inertia is a resitance to force. The only force involved here is centripetal force, which is the force applied by the bucket onto the water in the direction toward your hand at the end of the rope. This force is caused by centripetal acceleration.

In the case of orbiting satelites, gravity is the centripetal acceleration and the horizontal speed of the satelite is the inertia. There is no force directed away from planet Earth that is holding the satelite in orbit. Just inertia and centripetal acceleration.

[GrapesOfWrath]

Centripetal means directed towards a center. So, a string whirling a rock around your head would impart a centripetal force to the rock--the tension in the string is a force directed towards your head, which is the center of the universe, of course.

Centrifugal ("fugal," from Latin, fugere, to flee) is "center fleeing." The above egocentric rock is not really fleeing your head, it is attempting to continue in a straight line. If you cut the string, it would attempt to continue in a straight line, tangent to the circle it'd been following, rather than in a straight line away from the center. That's why people say that there is no centrifugal force. On the other hand, most people understand that centrifugal force, in the reference frame of the whirling rock, is a reasonable concept. An ant on the close side of the rock would be pressed firmly against the rock, away from the center, and an ant on the far side would have to hold on tighter--so from the ant-perspective there appears to be a "center fleeing" force.

Years ago, I read a kids book biography, which I remember as being about Goddard, the pioneering rocket scientist. In the book, a boy is sick and confined to his room for weeks. He experiments with constructing a device to whirl a projectile around on a string, and insert a blade to suddenly cut the string. His first attempt was in front of his parents, before an open window. Of course, he cut the string just as the projectile was in front of the window--sending the projectile violently against the ceiling.

Anybody else ever hear this story? Who was it?

[ToSeek]

On 2001-11-15 08:11, GrapesOfWrath wrote:

Years ago, I read a kids book biography, which I remember as being about Goddard, the pioneering rocket scientist. In the book, a boy is sick and confined to his room for weeks. He experiments with constructing a device to whirl a projectile around on a string, and insert a blade to suddenly cut the string. His first attempt was in front of his parents, before an open window. Of course, he cut the string just as the projectile was in front of the window--sending the projectile violently against the ceiling.

Anybody else ever hear this story? Who was it?

I believe it was Goddard, but I remember it the other way around: he had carefully padded the ceiling so the projectile would do no damage, but when he cut the rope as the projectile was toward the ceiling, it of course went sideways, crashing through (and destroying) the glass window.

[GrapesOfWrath]

Couldn't find anything online, with goggle or altavista. This bio mentions an illness, and a revelation in a cherry tree (on a day he later referred to as "anniversary day"), but nothing about a window or ceiling.

<font size=-1>[Goddard did not call it "anniversay day"]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2001-11-15 11:05 ]</font>

[SeanF]

Okay, the discussions of whether "centrifugal force" is real, or an imaginary force, or what, are all fine and dandy, but I think everybody's missing the point of my original post.

Even if the term is acceptable when used to refer to the effect on spinning or revolving objects, it still doesn't apply here. There's no spinning or revolving, just the road curving out from under the car and the driver not making the turn -- it's just inertia, ain't it?

[GrapesOfWrath]

I took it to mean that the car is turning on the curve--hence the centrifugal force, directed out along the radius of the curve. The driver would sure feel it on the seat of his pants.

But I even had to look up the meaning of "bank", even though I've used it that way myself. When you think about what a "bank" is, how do you "bank" a car? It's a derived meaning, for sure.

[Donnie B.]

I was going to post and mention the "bank" thing too. Then I remembered how we all tend to lean into a sharp curve, and decided that was probably what they meant.

You can consider the sidewise force on the wheels of the car (keeping it on the road) as a centripetal force in this case. It's just like the tension in the string as you whirl the rock around your head, and with equally bad consequences if the string breaks (tires break loose from the pavement).

[Hat Monster]

I don't mind centrifugal force. It's a very real force if we take vectors from the point of reference of the object being acted upon.
Inertia acts as a force in the frame of reference of the object that's accelerating along a curved path.

Newton said it best: For every action, there is an equal and opposite reaction.
So if centripetal force is being applied, there's the equal and opposite.

[The Bad Physicist]

It is interesting to follow such a wonderful discussion about the causes to events that happen in the everyday world. I remember the heated debates we had as undergraduates trying to argue for and then against the literal existence of centrifugal force. We are all incredibly biased in our views of "what really happens" when one rounds a bend, I know I was at first.

When I was a kid, I would always anticipate the centrifugal force, as my brother would speed around the onramp. It was very real to me. The problem is, I was experiencing only half of the story. What I should have thought was: "Boy! I can't wait until my big brother Matt speeds around the curve, because from my point of view I will experience a pseudoforce in this noninertial reference frame."

Sometimes the word inertia gets pushed around without sufficient thought as to what it really means. Here is a good definition that I memorized in my analytical mechanics class: the tendency for an object to stay at rest or in uniform linear motion is what inertia is. Newton's first law can be called the law of inertia.

[The Bad Physicist]

Centrifugal force is another fun topic. It is a pseudoforce (someone mentioned "inertial force" which is right too), it exists only in noninertial reference frames. And pseudoforces are things that we create, a mathematical construct. So, classical mechanics explains things very well in inertial frames of reference. This is obvious because everything is obeying Newton's first law.

In the real world, there are plenty on things that appear in noninertial frames to us. If we are to apply classical mechanics to these noninertial frames and wish to make it consistent, then we need to establish some new entities. These are the pseudoforces that I mentioned with centrifugal force being the most famous. The name says it all. We cannot relate these "forces" to any object in the system hence; they do not originate from anything. Also, they are not associated with the four fundamental forces. They are just mathematical "scaffolding" to help us explain physics within the noninertial reference frame.

As for an observer outside the car, that is, in an inertial frame, he/she observes no pseudoforce (centrifugal force). When the car rounds the bend, they just see the person inside the car trying to obey Newton's first law. That is, the person in the car wants to keep moving in uniform linear motion tangent to the motion of the car.

[David Simmons]

On 2001-11-15 14:57, Hat Monster wrote:

Newton said it best: For every action, there is an equal and opposite reaction.
So if centripetal force is being applied, there's the equal and opposite.

I don't think so. Isn't the reaction to the application of centripetal force, the acceleration of the object toward the center in accordance with F = m*a?

[The Bad Physicist]

Yes, you're right. Keep in mind, I never said anything about the centripetal force. I only commented on the centrifugal force and its misconceptions. As far as centripetal force, it is indeed derived from Newton's second law (the classic equation of motion): ma=mv^2/r…Remember, my previous discussion was about centrifugal not centripetal force. Centripetal force is not a pseudoforce. It's a force that one can derive from Newton's second law. The Moon revolves around the Earth because of the centripetal force (gravitational pull) of the Earth on the Moon.

I agree with you when you say, "…there's the equal and opposite." It would have to be. If the internal forces between the person and the car are equal and opposite and lie along the line "joining" the two then we have action and reaction.

[Lusion]

On 2001-11-20 01:11, The Bad Physicist wrote:
The Moon revolves around the Earth because of the centripetal force (gravitational pull) of the Earth on the Moon.

I guess that's one way of thinking about it, but it seems oddly Euclidean.

The moon revolves around the earth, I propose, because its orbit is its inertial path. "Usually", inertial paths are in a straight line, but gravity bends said paths. Under this line of thinking, there is no centripetal force, and there's no inertial tendancy of the moon in a straight line (and there's no gravitational force either--it is a pseudoforce). This is, at the very least, how I understand general relativity to work.

Also, I have a general complaint about the analogy. If I take a bucket of water, and I sling it around by a string attached to the handle (carefully enough not to jar the water too much), then the water gets pressed against the bottom of the bucket. If the bucket were orbiting around the earth, the water wouldn't have such a push. So, my complaint is, I guess, that I don't believe an orbiting satellite is a good analogy to slung buckets or banked drivers.

[GrapesOfWrath]

On 2001-11-21 00:13, Lusion wrote:
Also, I have a general complaint about the analogy. If I take a bucket of water, and I sling it around by a string attached to the handle (carefully enough not to jar the water too much), then the water gets pressed against the bottom of the bucket. If the bucket were orbiting around the earth, the water wouldn't have such a push. So, my complaint is, I guess, that I don't believe an orbiting satellite is a good analogy to slung buckets or banked drivers.

I'm not sure I understand this complaint. When the bucket orbits the earth, the centripetal force (gravity) affects bucket and water both, whereas with the string, it affects the bucket which in turn affects the water. Is that why you don't like the analogy? Still, I don't see why that is too misleading.

[Lusion]

On 2001-11-26 12:53, GrapesOfWrath wrote:
I'm not sure I understand this complaint. When the bucket orbits the earth, the centripetal force (gravity) affects bucket and water both, whereas with the string, it affects the bucket which in turn affects the water. Is that why you don't like the analogy?

Yes, it's that simple. The situation is just different. It could mislead me if I didn't know better, because I would think that there should be a fictitious centrifugal force on the moon as well that's due to the moon's inertial tendancy to go straight. Of course, fictitious treatments of gravity aside, this isn't the case because of gravity's nasty tendancies to act on all objects at once and to conveniently increase proportionally with the mass. But it doesn't intuitively follow from the analogy why there is no centrifugal force on the earth side of the moon.

I prefer thinking of orbits as falling objects, or objects travelling warped inertial path. This creates a better intuitive picture than thinking of gravity as an invisible string.

Technically, I think the explanation works (if we don't treat gravity as fictitious)--thus, I didn't say it was a wrong explanation. I just think it's potentially misleading because it's so different.

[GrapesOfWrath]

Yeah, if you're going to complain about centrifugal force being fictitious, then to be consistent, you're also going to have to complain about centripetal force (gravity) being fictitious.

Centrifugal force is real to the water in the bucket, right? Just ask anyone in a centrifuge.

[amstrad]

On 2001-11-28 04:16, GrapesOfWrath wrote:
entrifugal force is real to the water in the bucket, right? Just ask anyone in a centrifuge.

No. There is no force pointing from the center of the cetrifuge out. The force one feels in a cetrifuge is centripetal, and it points toward the center. This force causes an acceleration toward the center and hence the cirular motion. Forces are not equal and opposite when accelerations are involved, which is certainly the case here.

Once again, inertia is NOT a force.

[GrapesOfWrath]

::smilies enabled, just this once::

On 2001-11-28 08:12, amstrad wrote:
No. There is no force pointing from the center of the cetrifuge out. The force one feels in a cetrifuge is centripetal, and it points toward the center.

Wait...then, gravity points up??? [img]/phpBB/images/smiles/icon_smile.gif[/img]

This force causes an acceleration toward the center and hence the cirular motion. Forces are not equal and opposite when accelerations are involved, which is certainly the case here.

Relative to the bucket, there is no acceleration. That's the whole point of using alternate reference frames.

Once again, inertia is NOT a force.

Thanks, I needed that. No need to shout though.

[Irishman]

Ugh. People keep mangling the "equal and opposite" force statement by Newton. Centripetal and centrifugal are not equal and opposite forces under Newton's definition.

What his statement really means is that a force cannot act solely upon one object, but equally reacts between two objects. You push on the wall, the wall pushes back on you. The water in the bucket pushes on the bucket, the bucket pushes back on the water. The moon pulls on Earth, the Earth pulls on the moon. Tension in a rope pulls both ends. That is the equal and opposite force in question.

[Lusion]

On 2001-11-28 10:47, Irishman wrote:
Ugh. People keep mangling the "equal and opposite" force statement by Newton. Centripetal and centrifugal are not equal and opposite forces under Newton's definition.
...
The water in the bucket pushes on the bucket, the bucket pushes back on the water.
...

Isn't this kind of contradictory? After all, why does the bucket push back onto the water instead of going straight? It seems to me that's where the centripetal force comes from. That also implies that the water's pseudoforce against the bucket qualifies as centrifugal.

I do agree, however, that the original description was pretty loose--IOW, I agree that there's no centrifugal force just because there's a centripetal force (like everyone says, it's the inertia!)

[Irishman]

Gad, I give what I think is a simple explanation and someone has to purposely misconstrue what I said.

Lusion, if the water pushes on the bucket, there is no way the bucket cannot be pushing back on the water. It does not matter if the bucket is restrained by the rope or not. The bucket can be in free fall and the water ejected by a water cannon, when the water strikes the bucket, it pushes the bucket, and the very nature of forces is that they push both sides. That is what Newton was saying.

If I push a door open, the push is also against my hand. Sure, the door opens, but the contact is between two objects - door and hand. Does not matter the effect of the force, the fact that there's a force means both sides feel it. Now if the door moves easily, it takes less force to open, but that force is still a two-way force between the door and my hand.

I don't know how to say it any plainer than that.

You are correct that if the bucket is restrained by a rope or my arm or some other manner so it curves in a circular path, then the force pulling the bucket is centripetal. But that coordinate system is not the bucket, it is the center of the curve (i.e. me), so the water is not experiencing a centrifugal force. The force on the water is the bucket pulling in.

If you jump and use the bucket as your reference point, then yes, you can describe it's inertia as a centrifugal force, but in that case the bucket is not experiencing a centripetal force. It is either being pulled inward, or it is being pulled outward.

[Lusion]

On 2001-11-29 12:10, Irishman wrote:
...

You're still saying the following:
1. If there's a force (water pushing on the bucket) acting on an object, then there's an equal and opposite force in the other direction.
2. That this is Newton's law.
3. That pulling on the bucket is centripetal force.

All contended.

4. That the water doesn't push back on the bucket, unless you translate coordinate frames.
5. That this has nothing to do with centripetal vs centrifugal force.

Points 4 and 5 are where I disagree.

I'm not sure what you are saying here:

But that coordinate system is not the bucket, it is the center of the curve (i.e. me), so the water is not experiencing a centrifugal force. The force on the water is the bucket pulling in.
...
It is either being pulled inward, or it is being pulled outward.

..but it seems to me that this is the key to your point. However, it also seems to me that you are saying that the water does not in fact push on the bucket--that the bucket pulls the water only. That's what I'm pointing out that seems so contradictory. First you say that every action has an equal and opposite reaction--then you say that, well, in this case, pulling is the action, and there's no real push because the action is pulling. Either every action has an equal and opposite reaction or it doesn't. Either the water pushes back or it doesn't. Either the water's pushing back is an equal and opposite reaction to it's being pulled in, or it isn't. Which is it? Or if there's something I'm not seeing, please point it out.

[Ducost]

A picture would be helpful right about now.

[David Simmons]

The bucket pulls inward on the water and the water pushes outward on the bucket and those two are in equilibrium at zero acceleration relative to each other.

The (massless) rope pulls inward on the bucket (and the water which is in force balance with the bucket) which reacts with a central acceleration of W^2*r. W is the angular velocity of rotation and r is the radius of the turn.

At the other end of the rope, it pulls outward on the pivot point thus leaving the rope with no net translational force on it.

And finally my hand, or whatever, pulls inward on the pivot point so it doesn't move.

The only unbalanced force is the inward pull on the bucket and that is what gives the bucket its acceleration.

Forces are only in balance in the case of constant velocity. Unbalanced forces result in acceleration. Newton's laws do not say that a force is always opposed by another force. An action is opposed by an equal and opposite reaction is the statement, not that a force is always opposed by an equal and opposite force.

In my physics books the first two laws both specifically refer to unbalanced forces.

First Law: A body continues in its state of uniform motion (or rest) unless acted upon by an exterior, unbalanced force.

Second Law: An unbalanced force acting on a body causes the body to accelerate proportional to the force and inversely proportional to the mass of the body.

Third Law: For every action there is an equal and opposite reaction.

<font size=-1>[ This Message was edited by: David Simmons on 2001-11-29 23:19 ]</font>

[The Bad Physicist]

What a controversy this has become. When I posted on the first page, I wanted to clear up the misconceptions about centrifugal force but it seems like a lot people want to make it something more that it really is. There are no mysteries involving centrifugal force, only curiosity and an occasional misunderstanding. If one wants to learn more about centrifugal force and general concepts of mechanics, judging by all the replies, one is better off reading "Analytical Mechanics" by Fowles and Cassiday or any number of great mechanics books...