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# Centrifugal force

I know that some of you folks are aware of this, but some of you may not be. Just FYI:

There is no such thing as "centrifugal force." And in the manner in which some of the folks here are using this term, that force they are describing does not represent a true physical force.

"Centrifugal force" is a pseudo-force, an illusion that is the product or result of inertia.

Newton's First Law informs us that mass, once moving in some direction with some velocity, will continue to move in a straight line in the same direction with the same velocity unless some external force acts upon it to bend its path, speed it up, or slow it down. This is inertia, the underlying principle that produces the "centrifugal force" effect.

If you are in a car that turns a corner, inertia is what causes your body to try to continue in a straight line. Forces exerted by the seat, the seat belt, the doors, tires, car frame, etc. are required to push your body in the new direction. Thus, you have the illusion (because your point of view is in a reference frame that is being accelerated in a circle) that some external force is "building up" to "push you away" from the center of the turn. There is no such force.

What you actually experience is inertia trying to continue your motion in a straight line while the structure of the car around you is moving in the circular path of the turn.

As I mentioned, I realize that at least some of you folks know this already... but it's possible that some of you may not... so I offer this post in that spirit. It may seem like splitting hairs, but I do think it's important to be clear on certain concepts if we're going to teach them... and that includes knowing the difference between "centrifugal force" and "inertia."

Thanks for your time and attention!

:::: running and ducking for cover ::::

### You could have just bumped the old thread up, ya know.

Some comments on centrifugal and centripetal force

Quote:
Quote:
 Originally Posted by Baja I know that some of you folks are aware of this, but some of you may not be. Just FYI: There is no such thing as "centrifugal force." And in the manner in which some of the folks here are using this term, that force they are describing does not represent a true physical force. "Centrifugal force" is a pseudo-force, an illusion that is the product or result of inertia.:::: running and ducking for cover ::::
I'll run and duck with you if that's OK with you. An instructor friend of mine refers to this as "an easily understood falsehood".
I am greatly concerned about this while skiing. At one point, I decided that it didn't exist and I immediately fell over right in the middle of a turn; then, I changed my mind.:

Happy New Year
Quote:
 Originally Posted by comprex You could have just bumped the old thread up, ya know.Some comments on centrifugal and centripetal force

But I wrote it so much better, comprex.

(Brilliant, sexy stud that I am.)

:::: ducking back down for cover ::::

### Nothing is real

Quote:
 Originally Posted by Baja Newton's First Law informs us that mass, once moving in some direction with some velocity, will continue to move in a straight line in the same direction with the same velocity unless some external force acts upon it to bend its path, speed it up, or slow it down.
Velocity measured from what reference point? The ground, a spot between your eyes, your centre of mass, the sun, Galactic Centre, Galifrey, the deck of a ship, the surface of the left ski? All are perfectly valid points of reference (well with the possible exception of Galifrey).

Newton's 2nd law says that acceleration will equal the sum of all the forces acting on the object divided by it's mass. If you are using a reference point such as your c of m, then there surely must be a centrifugal force or F=MA would not work!

Of course gravity is not a real force and space is curved, but is space REALLY real?
Baja--with all respect, please dig back into your physics books. Centrifugal Force most certainly does exist. It is a real force, a "true physical force."

You are correct that it is a function of inertia. Centrifugal force is an inertial force. That is to say, it results from acceleration (turning, in this case) rather than causing it. But it is no less real, no less significant, no less measurable than the motive force that causes turns.

It is a question of your frame of reference, as you have suggested. You are correct that, from the stationary (with respect to the earth) frame of reference of one observing a skier's turn, centrifugal force is not part of the equation of what is causing that turn, and that it may be passed off simply as an effect felt by the skier as a result of turning.

But from the "accelerated frame of reference" of the skier himself (or herself) in the turn, centrifugal force is most definitely a real force, acting on his body in a direction directly out from the center of the turn (perpendicular to the direction of travel at any moment in time). And since this is the frame of reference from which we actually experience our own ski turns, it is important to look at and describe the forces from this perspective. If you don't think it's real, trying making a turn without leaning in against it some time!

Understanding frames of reference and the relativity of motion is key to really understanding centrifugal force. It is worth pondering that, from your point of view as a skier (or anything else, for that matter), your frame of reference moves with you. That is to say, relative to you, you are not moving, not accelerating, not turning. You're always "right here," right? (Ask yourself at any time, if you're not sure!) So from your frame of reference, if there is no acceleration, there is therefore no "net external motive force"--which is to say that the forces you might normally call "real" are actually now "fictitious," and yet you do feel forces pushing and pulling you forward and back, left and right, up and down, and you need to move accurately to keep them all in balance. These are real inertial forces.

It depends entirely on your frame of reference which forces are causes and which are (merely?) effects. Either way, both are equally real! Fortunately, understanding the concepts intellectually is not actually critical for skiing well, as our bodies know all about it. But I've seen skiers who become so strongly convinced that centrifugal force does not exist that they've tried to change their movements based on that misunderstanding. Results can be comical!

For more on this, I encourage you to search the EpicSki archives. We've had many discussions about it. Search in particular for posts by "PhysicsMan" or "Tom/PM" (same person).

Best regards,
Bob Barnes
Wow--EpicSki is fast these days! None of those posts were there when I started writing my reply. Thanks, Comprex, for digging up that great Physicsman post that I was too lazy to search for. (Would have saved me time in the long run, I suppose!)

Tom/PM, as a professor of physics, does a phenomenal job of describing these technical concepts in lay terms, doesn't he?

Tom's points #11 and 12 are particularly notable--that it is essential not to mix frames of reference in a single analysis, and that it is usually considerably simpler to analyze the dynamics of skiing from the stationary observer's point of view (in which centrifugal force is not a force acting on the skier in the equation), but that it can be useful to look at the skier's accelerated frame of reference as well.

Unfortunately, as I noted above, the simpler analysis from the "stationary" frame of reference doesn't usually help understand or explain ski technique as obviously as other frames of reference might. We experience our ski technique from our own accelerated frame of reference, not that of a bystander, so to understand the forces we feel and deal with in a turn, I think it is more obviously relevent, if not actually simpler, to analyze the forces from that perspective.

Fascinating subject, in any case, at least I've always thought so! It is amazing how often the argument comes up in skiing terms. "Centrifugal force exists." "No it doesn't." "Yes it does." Etc. Both may be right, but both may be wrong! They seldom realize that they are arguing from opposite frames of reference.

Best regards,
Bob
Quote:
 Originally Posted by Bob Barnes/Colorado Baja--with all respect, please dig back into your physics books. Centrifugal Force most certainly does exist. It is a real force, a "true physical force."
According to the American Heritage Science dictionary:
Quote:
 An effect that seems to cause an object moving in a curve to be pushed away from the curve's center. Centrifugal force is not a true force but is actually the effect of inertia, in that the moving object's natural tendency is to move in a straight line.
According to the regular American Heritage Science dictionary:
Quote:
 The apparent force, equal and opposite to the centripetal force, drawing a rotating body away from the center of rotation, caused by the inertia of the body.
With all due respect, the definition of Centrifugal Force all depends on your (frame of) REFERENCE.
Rusty--that's why I've never seen a dictionary used as the text for a physics course!

Best regards,
Bob
Okay Bob, it really pains me to admit how long it's been since I've been in a physics class, but 30 years ago my texts (which for some strange reason are not online) described centrifugal as a psuedo force. There have been many updates to physics since then, but if this has changed I did not get the memo from Physicsman.
There really is no such thing as a pseudo-force...a force is a force..if something pushes or pulls on you it is real...it doesnt matter if it is getting slammed to your seat at the bottom of a hill on a roller coaster or dropping a rock on your foot.

Anyways this being said centrifugal force is a force by defintion of what a force is.

Force is IMPLICT in Newtons laws..not EXPLCIT. Newton did not set out to define what a force is or is not...he set out to define the dynamical relationship between the position in space relative to a fixed reference frame, velocity, acceleration, and the implicit property of inertia which is implicitly defined in Newton's laws of motion as resistance to change in direction or velocity..

i.e. the natural state of an object is to remain at rest or uniform motion..this is the very heart of Newtons Laws...this implies the object will resist a change to its natural state no?. What is this inherent property of things that resists this change to its state? We call it inertia.
The idea of inertia goes hand in hand with the idea of force. It gets a bit more complicated when gravity comes into the picture as there are 2 different defintions for inertia.

Anyways resistance needs to be overcomed to bring about a change in this state. This is implicitly defined as the force...since the force required is the same as the resistance we arrive at the idea of 'equal and opposite forces'. If you push on something it pushes back just as hard with as just much force. Newtons laws flow naturally from one to the other. Inertia goes hand in hand with the notion of force...

Anyways....acceleration is not a scalar quantity. Acceleration has both a vector and scalar component. The absolute value of the scalar component can remain 0 but if the gradient of the vector components is non zero there will be a resulting acceleration and effectice force in opposition. If centrifugal force is not real Newton would never have arrived at the Theory of Universal Gravitation and we would not be here because the solar system would be one giant point of rotating gas.

..ps.. this is semantics but you might be confusing the term 'centripital' with centrifugal..the acceleration of a particle undergoing change such as in an orbit about a fixed point is centripital acceleratioin...the centripital acceleration vector is actually perpindicular to the plan of rotation. but there is no centripital force...it is called centrifugal force and the vector points inward.
Quote:
 Originally Posted by JackFrost There really is no such thing as a pseudo-force...a force is a force..if something pushes or pulls on you it is real...it doesnt matter if it is getting slammed to your seat at the bottom of a hill on a roller coaster or dropping a rock on your foot. Anyways this being said centrifugal force is a force by defintion of what a force is.
The definition of force:
Quote:
 an influence on a body or system, producing or tending to produce a change in movement or in shape or other effects.
The definition of inertia:
Quote:
 a.the property of matter by which it retains its state of rest or its velocity along a straight line so long as it is not acted upon by an external force. b.an analogous property of a force: electric inertia.
The definition of pseudo:
Quote:
 not actually but having the appearance of; pretended; false or spurious; sham.
If centrifugal force is really inertia, it's not really a force. A pseudo force is only apparently a force because of a frame of reference. This is what my dictionaries and my physics books taught me. Feel free to disagree. It all depends on YOUR frame of reference.
It's all been said before, but perhaps not in the right way, as you still don't seem to get it. Let me try again.

You are inside a tractor trailer. You have a mass that is accelerating. By that, I mean that it's velocity is changing. You know it's velocity is changing because you have laid out a measuring tape along the length and width of the trailer and have a stop watch. Let's say it was rolling straight ahead, and now its velocity is no longer straight ahead, but it has curved to the right. Imagine you are inside the tractor trailer and bowling a ball to the front of the trailer. Case 1 the ball goes straight to the front of the trailer (we will ignore the slight slowing down due to friction). Case 2 the ball careens off and strikes the right wall. The ball in case 2 is accelerating; it's velocity is no longer straight toward the front of the trailer.

According to Newton's 2nd law, F=ma, a force has caused this acceleration. Without this force, the ball would not accelerate. This force is REAL, just as real as the gravity force that keeps the ball pressed against the floor. You know the gravity force exists because the ball is accelerated towards the floor when you drop it. You know the other force is real because the ball is accelerated to the right.
Inertia is the property of mass that resists acceleration. A body remains at rest because of it's inertia. "At rest" means not moving with respect to some "fixed" point. There is no absolute fixed point! At rest with respect to one fixed point is not at rest with respect to another point that is accelerating relative to the first fixed point. One frame of reference has a body at rest with no force acting on it, the other has a body accelerating with a force acting on it.

All frames of reference are arbitrary, the differentiation between a real force, or no force does indeed depend on what frame of reference you use. If you have a force it is real, but it may not exist in the other reference frame.

If you see things from the point of view of the ground, then there is no centrifugal force in a skier turning, though a centripetal force does make him turn, and there is an equal and opposite force acting on the snow. If you see things from the point of view of the skier (zero,zero moves with the skier) there is a force pushing him to the outside, and the force counteracting that force and thus causing him to remain stationary is the normal force of his skis pushing on the snow.
JackFrost: A couple of slipups: There is but one "inertia": resistance to movement (be it linear or rotational). There are, however, two kinds of "mass": inertial and gravitational.

The vector perpendicular to the plane of rotation is that of "angular momentum"; more properly, the vector cross-product of torque and the radius of movement.

Ghost: I think you were trying to say that something would seem to be moving or not moving depending on which inertial (constant velocity) frame of reference was used. In an accelerating frame, however, measured object's paths will seem to be influenced by "pseudo" forces.

While it may be convenient to pretend there is a centrifugal force, it is no more a "real" force than is, say, the Coriolis effect (another psuedo-force seen in rotating frames).

PhysicsMan is correct that forces are always "action-reaction pairs" and each force acts on just one body, not both.

I believe Newton originally did not cast his laws in terms of "force" but "acceleration" alone. In some ways, that is a better way of understanding what is called the "centripetal acceleration" because the concept of "force" (mass * accel) sort of blurs what is happening. Just focusing on the "acceleration" is enough to understand the concept of why something is taking a curved path without having to resort to "force".

Then, too, a "centrifugal" force vector isn't all that useful: exactly what path will a body take when you apply one? At least with the rotating centripetal vector you can see a curved path results.

This whole centrifugal thing comes about because we feel a "weight-like" action on our body when we take a circular path: yet no one seems to need a special name for the "weight-like" feeling we get when taking off in a car or when in an elevator. Yet all those situations are exactly the same.
I am a little sorry I started this thread... despite the fact that it's become quite informative, and perhaps productive.

My apologies. (although some folks may not feel it's necessary for me to offer them)

Like so many other concepts in science and philosophy, this issue of "centrifugal force" is a still-unresolved issue. And like rusty, my conclusions are based on information in my physics texts and resources (one of which is a military pilot's training manual)... as well as my education from high school, college, and graduate school.

I first became aware of this argument years ago as I was pursuing PSIA Certification, and one of the part-time instructors I worked with (physics major college student) suggested to a group of us, as we were studying/reviewing in the cafeteria, that "there is no such thing as centrifugal force." If I remember correctly, everybody in the group "pshawed" him and told him he was off is rocker. (Particularly because it said "centrifugal force" right there in the PSIA manual. So it must be true!!! )

A lengthy discussion ensued, over the course of several weeks, and my understanding and conclusions started to change.

As I see it, all the academic nuances of this subject don't necessarily play a vital role in skiing mechanics and instruction... other than to recognize that the forces we are attempting to describe and label are physical forces that are real and observable. I don't think anybody here believes that the "centrifugal force" being described here is "imaginary" or "fake."

IMO, I do believe "pseudo-" is an appropriate description where it's been used in this discussion, recognizing that "pseudo" means "resembling" or "having the appearance of" ---- indicating that these forces are real, but are attributed to something else besides the "creation" or "appearance" of a "centrifugal" force.

Nevertheless... in keeping with my New Year's resolution of being a bigger person (socially and psychologically), I have a new-found interest in investigating the issue further, (as I'm not dead-set on my conclusions) and will continue to do so.

Particular thanks to Bob Barnes for your explanations and viewpoints.
Bsather,
How do you know which frame of reference is accelerating. What is your frame of reference for judging this? All frames of reference are accelerating with respect to some frame of reference, and not accelerating with respect to others.

We almost concur. Let's consider a ball in the middle of an elevator near the surface of Earth, an elevator that is accelerating downwards at 9.8 m/s/s. You say "in an accelerating frame"...Let's call it frame A, based on the elevator floor. Which frame is accelerating and which one is not? Acceleration itself must be based on a frame of reference. If you see frame A as an accelerating frame or reference, i.e. accelerating (at 9.8m/s/s ) with respect to some other frame B (based on the ground), you are seeing it from outside frame A, and the object is in fact obeying the laws of inertia in frame B by accelerating at 9.8m/s/s with net force due to gravity acting on it.

However from the point of view of someone who judges acceleration and all other motion based on frame A (which you view as accelerating with respect to frame B), then the net force must include gravity and an upwards force equal to gravity so that the object has no net force acting on it, as it is clearly not accelerating using that frame (A) of reference.
Quote:
 Originally Posted by bsather JackFrost: A couple of slipups: There is but one "inertia": resistance to movement (be it linear or rotational). There are, however, two kinds of "mass": inertial and gravitational. The vector perpendicular to the plane of rotation is that of "angular momentum"; more properly, the vector cross-product of torque and the radius of movement. Ghost: I think you were trying to say that something would seem to be moving or not moving depending on which inertial (constant velocity) frame of reference was used. In an accelerating frame, however, measured object's paths will seem to be influenced by "pseudo" forces. While it may be convenient to pretend there is a centrifugal force, it is no more a "real" force than is, say, the Coriolis effect (another psuedo-force seen in rotating frames). PhysicsMan is correct that forces are always "action-reaction pairs" and each force acts on just one body, not both. I believe Newton originally did not cast his laws in terms of "force" but "acceleration" alone. In some ways, that is a better way of understanding what is called the "centripetal acceleration" because the concept of "force" (mass * accel) sort of blurs what is happening. Just focusing on the "acceleration" is enough to understand the concept of why something is taking a curved path without having to resort to "force". Then, too, a "centrifugal" force vector isn't all that useful: exactly what path will a body take when you apply one? At least with the rotating centripetal vector you can see a curved path results. This whole centrifugal thing comes about because we feel a "weight-like" action on our body when we take a circular path: yet no one seems to need a special name for the "weight-like" feeling we get when taking off in a car or when in an elevator. Yet all those situations are exactly the same.
Yes I wrote post too quickly....too many brewsky...it is inertial and gravitational mass...

was trying to make the point that inertia is a property we assign to matter to account for the way matter behaves...whether in a gravitational field or when undergoing a force or lack thereof.

Did my masters Thesis on this subject(Newton, Boyle, Hooke) in Phil of science at Pitt. Most people when they think of Newton is the parable of the Apple(a folk tale actually like Washington and cherry tree)...

If you read Newton and his correrspondence with others - Hooke, etc what he found most striking about nature was the sublime.... In a nuthsell the fundamental and most striking property to netwon was not what Nature does but what Nature does not do..Like many an artist who draws by thinking of the space surrounding the object rather than the object itself Newton looked behind what was seen and obvious before our eyes. There he found the answers.

What do I mean? Something so subtle and obvious: set down an object and come back the next day and it appears the same, has the same position etc etc..obvious and trivial? To us yes...to Newton no. Why when all of nature appears to be in flux would such a constant appear? It is a very striking question when looked at closely and was actually the impetus(no pun intended) for Newtons concept of Inertia and first law....

basically nothing moves unless moved...when first read in a physicst text we say 'uhh...yeah ok..so obvious..so what..why mention it?'...so trivial to us but actually the first to think it through to such a degree and it lead to the resulting framework in the principia. Everything else in Newton's framework proceeds from this simple, obvious, and yet so profound princple of inertia - matter has a property and this property gives the appearance of resistance to a change of state...in this case of stationary object with respect to a fixed coordinate system it resists translation. All other concepts of mechanics-momentum, force, etc etc all proceed thus. Fascinating ! Rightfully so the first law Newton surmised.

.Regarding skiing look at it this way...if you do anything to change your orientation, position, velocity, relative to the snow beneath you then you will 'feel' the effects because your body parts, skis, and the snow all resist this change in unison. You feel the 'force' Luke.
Oh come on now. Centrifugal force is the radial addition of inertial force countered by centripital force. Everybody know that if we accept that things are Newtonian at the time we are describing. Of course this does not take into account the square root of a rats ars as I givea damn. Remember the ol rope and bucket example? I think cgieb summed it up best.

From one Injinear to another. Let it rest.
Ghost: The accelerating frame is the one in which you notice the acceleration!

What that means is that all of a sudden you would notice that momentum is seemingly not conserved. This is the key point.

That is because, from the standpoint of observers not in the accelerating frame, everything in the frame is gaining or losing momentum.

The "outcome" of a momentum change is a "force". The classic example of this is the "Coriolis force", a psuedo-force that manifests itself in rotating (and thus accelerating) frames. So in any accelerating frame you will see "forces" suddenly appear as if from nowhere.

Now, it is true Newton based his laws on an assumption that there is a "universal fixed point" from where all velocities could be measured (thus, the concept of the "ether" developed). Of course, after the M-M experiment it was pretty obvious there was no ether and then Einstein kissed the whole fixed-point idea goodbye. So, in practice, there are probably no true non-accelerating inertial frames.

How do you tell who is really doing the accelerating? By measuring the action-reaction pairs. In the case of the elevator, the action-reaction pair of the ball resting on the floor will appear to be "weightless" because the ball is unable to exert any force on the floor as it is moving away as fast as the ball is falling so that the relative acceleration is zero and thus the F=ma is zero.

Similarly, in a car you will be able to tell that you are accelerating towards the wall rather than the wall towards you.

Take the bucket on a rope. Say you were living on the surface of the water in that bucket. Say the bucket was just hanging from a tree (normal gravity). Say you tossed a ball in the air. It would come straight down. Now let's get you spinning by somebody whirling the bucket around in a circle (let's say he did this in space so gravity is no longer a factor). Now you toss the ball. It won't come straight down. Now you know you are in an accelerating frame by the appearance of a "pseudo-force" that moved the ball off course.
Quote:
 Originally Posted by JackFrost Regarding skiing look at it this way...if you do anything to change your orientation, position, velocity, relative to the snow beneath you then you will 'feel' the effects because your body parts, skis, and the snow all resist this change in unison. You feel the 'force' Luke.
So its ok to say that once you start turning there will be be a centrifugal force pulling you towards the outside of the turn and that you can resist this force by edging your skis and shifting your CoM into the turn?
Quote:
 Originally Posted by tdk6 So its ok to say that once you start turning there will be be a centrifugal force pulling you towards the outside of the turn and that you can resist this force by edging your skis and shifting your CoM into the turn?
You could, but technically, what is happening is that you a tending to go in a straight line (first law) and you want to alter that course by moving in a curve (second law). You sense the tendency to go in a straight line as the "centrifugal force", and you counter that with a true force, the centripetal force, by edging and CoM movement to as to turn.
Quote:
 Originally Posted by bsather You could, but technically, what is happening is that you a tending to go in a straight line (first law) and you want to alter that course by moving in a curve (second law). You sense the tendency to go in a straight line as the "centrifugal force", and you counter that with a true force, the centripetal force, by edging and CoM movement to as to turn.
Thanks, conclusion: while turning there is something we call a centrifugal force pulling on us towards the outside and a centripetal true force we create ourselfe by digging in those edges and leaning into the turn.
Quote:
 Originally Posted by tdk6 So its ok to say that once you start turning there will be be a centrifugal force pulling you towards the outside of the turn and that you can resist this force by edging your skis and shifting your CoM into the turn?
Correct!

Using the frame of reference from which you measure all things, defining a spot marked on your belly button as having zero velocity, a true body force will attempt to pull all things towards the outside of the curve. To avoid bing pulled to the outside of the curve and maintain your position of rest, you must apply a force to the snow and the normal force pushing back on YOU negates the body force. a=F/M=0.

What Bsather is doing is using the frame of reference of the ground to define the motion of the skier and a skier's accelerating frame of reference.

"what is happening is you are tending to go in a straight line (with reference to the ground)", "and you want to alter your motion by moving in a curve (with reference to the ground again)". Bsather sees what is really happening as what is happening as defined from a ground based reference frame. It is an excellent translation of what is happening in the skier-fixed frame of reference to a frame of reference based on the ground. The centrifugal force does indeed not exist in the ground-based reference frame.

It is hard for some people to let go completely of their habitual frame of reference. You should only use ONE frame of reference at a time to define your motions and forces, and adopt it fully completely. In the skier-fixed reference frame you do not want to travel in a curve; you want to avoid being pulled to the right by a body force.

The difficulty of letting go of the ground-based system, is why PM recommends using a ground based frame of reference. I have no qualms about which reference frame is real; they are all equally valid MODELS, none are what is really happening.
Quote:
 Originally Posted by tdk6 Thanks, conclusion: while turning there is something we call a centrifugal force pulling on us towards the outside and a centripetal true force we create ourselfe by digging in those edges and leaning into the turn.
Not really. .nothing is pulling you ...its simply inertia...your body wants to keep moving along a tangent and does not like to be displaced from the current state..in this case it is simply resiting the effort to change direction..the same applies to the skis or any other mass...this is felt as a force.
Quote:
 Originally Posted by JackFrost Not really. .nothing is pulling you ...its simply inertia...your body wants to keep moving along a tangent and does not like to be displaced from the current state..in this case it is simply resiting the effort to change direction..the same applies to the skis or any other mass...this is felt as a force.
Note that I was using simply "force" for the cetrifugal force and "real force" for the centripetal force. Should I completely drop the word force for the centrifugal thing and just call it something else. All I know is that if we have a force one way we need an other force of same value the other way (if nothing moves).
Tdk6,
Either there is a force or there isn't. There is no Pseudo to it.
1) Choose your frame of reference.
2) Forces are what add up to mass times acceleration.

Example 1: Frame or reference based on coordinate system pinned to the ground: The skier's motion accelerates, describing a curved path to the right. The forces acting on the skier add up to a force that causes the skier to turn to the right. This net force is a centripetal force. The forces involved are gravity (pointing at the centre of the Earth), a force acting on the snow at the ski/skier-snow interface which does not affect the skier's motion, and a reaction force (Newton's 3rd law) acting on the ski/skier at the ski/skier-snow interface. These forces add up to a net force to the right.

Example 2: Frame of reference based on coordinate system pinned to helmet cam mount of skier. The skier is not accelerating, but stays put in a single position not moving with respect to the helmet cam mount. The forces acting on the skier are gravity, the centrifugal force acting to the left, the force of the snow acting on the skier (pushing right). These forces add up to zero.
Quote:
 Originally Posted by tdk6 Note that I was using simply "force" for the cetrifugal force and "real force" for the centripetal force. Should I completely drop the word force for the centrifugal thing and just call it something else. All I know is that if we have a force one way we need an other force of same value the other way (if nothing moves).
The force is real - you feel it. What I am saying is there is not a 'force' that initiates the displacement. The force of centripital acceleration is a result of the inertial properties of the mass resisting the change in direction. Your body wants to keep going straight and your skis are turning so your body mass presses into the ski giving the resulting feeling of being 'pulled' towards the center of the arc. In other words your body wants to keep going straight but the positioning on the skis prevents it from doing so and the result is you get 'mashed' into the ski.
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