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Centrifugal force and newton 3rd law

  1. Jun 27, 2008 #1
    Ok, I have a general question about centrifugal force.

    Lets say I have an object who moves in a circular path, we know the object is accelerating because the velocity is constantly changing direction, the acceleration is towards the center.

    Now, where does the centrifugal force comes to play?
    Is it equal to f = m*w^2*R = m*v^2/r ?
    Does it comes from newton 3rd low to the centripetal force?

    10x in advance.
  2. jcsd
  3. Jun 27, 2008 #2
    There is no such thing as centrifugal force. My university physics professor taught me that in the 1970's. The force equations you quoted are for centripetal force, which are correct. BR.

  4. Jun 27, 2008 #3
    I was taught that the term centrifugal force was the reaction to a centripetal force encountered in applying it.

    For example, your moving mass was forced to take a circular path because of a constant centripetal force directed toward the circle centre. Now if this force was delivered via a string by which it was tethered to a central point, the anchor then experiences a force apparently directed outward away from the centre. ie. exactly equal and opposite to the centripetal, it being the reaction.

    Centripetal is the true mathematical abstract force concept. It is the force that did the work to effect the acceleration (in this case as a constant changing of direction), and has to be directed inwards. Centrifugal refers to what is experienced in getting that force applied - a consequence.

    This whole thing gets close to what we mean by "force". You know what it is when you feel it, but darn that it can only be conceived and defined in terms of its effects. It is "that which" can do work, "that which" causes acceleration to a mass, "that which" drags you to the ground. Its always "that which". The math definition is very fine, but I accept that the pulls and tugs on us can cloud how many names we need for it.
  5. Jun 27, 2008 #4


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    Using the "classic" definition, centrifugal force, is the inertial reaction force to the centripetal force that is accelerating an object inwards.

    Some time ago, physicists decided to change the meaning of "centrifugal" to mean an apparent force when observered from the rotating objects frame of reference. So the old one got a prefix, "reacitve centrifugal force", and "centrifugal force" was changed to the "modern" version.

    "Classic" - http://en.wikipedia.org/wiki/Reactive_centrifugal_force

    "Modern" - http://en.wikipedia.org/wiki/Centrifugal_force
  6. Jun 27, 2008 #5
    If you are not using rotating frame of reference, then there will not be any centrifugal force. That means, if your coordinate set is stationary, and the object moves in a circle in this frame, there is no centrifugal force.

    If you choose to use a rotating coordinate set, so that the object is stationary in the coordinate set, and the coordinate set itself is rotating, then there will be a centrifugal force, which points outwards from the center. In this case the formula

    gives the magnitude of the centrifugal force correctly.

    It could be your are on right track, although I cannot be fully sure what you are meaning. If we assume that the Newton's laws to hold without pseudo forces in inertial frames, and then demand that Newton's laws must hold somehow also in non-inertial frames, we can have the demand satisfied by solving what kind of pseudo forces we must add there so that the F=ma would be satisfied. In this case the centrifugal force is put in to cancel the centripetal force.
  7. Jun 27, 2008 #6
    I guess we all could have visited the Wiki first, but my thanks Jeff R. for the links. I never knew there was a deliberate effort to resolve the names.
    I think one cannot hold that the concept, complete with origin name was simply a fiction! The name, with its Latin origin, is historically quite old. Along with pilots, and drivers and trapeze artists, we can all appreciate how such force was experienced, described, and named. Understanding what it is, we should not be zealots about banishing it from out vocabulary - even if Mr. Newton et al were referring to its effect on moving masses one stage removed from the physical reality of applying it!
  8. Jun 27, 2008 #7
    I'm not sure if I like the "reactive" article completely. First let me clarify something for the OP:

    If you have a particle moving in uniform circular motion, then there is a centripetal force which is that equation you have listed. By Newton's second law, this is the only force acting on the particle; there is no centrifugal force.

    The definition of the centrifugal force as an apparent force that tends to throw one outward while in a rotating frame of reference. This is why it is sometimes called a fictious force - because it appears only to the observer in the non-inertial frame (i.e. the rotating frame of reference).

    The best example is you in a car that is moving at constant tangential velocity in a circle. From your frame of reference, there must be something that pushes you against the side of your car - you call this the centrifugal force. But how about myself, who is miraculously floating overhead and stationary?

    From my frame of reference, at a single instant, you are moving in a straight line in the direction of the tangential velocity while the car is moving in a curved path. An instant latter, the side of the car comes crashing into you causing you to change your path. So from my frame of reference, no force whatsoever pushed you into the side of your car - you and your car just so happened to have colliding paths.

    Regarding the "reactive" centrifugal force:
    This will be manifested as a consequence of Newton's third law in reference to you and the side of your car coinciding. I must say though, I've never heard this term before and don't necessarily know if I like it yet....
  9. Jun 27, 2008 #8


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    non-inertial observer

    Hi asi123! :smile:

    On an object moving in a circular path, there is no centrifugal force as viewed by an inertial observer.

    Centrifugal force on such an object only exists for non-inertial observers.

    The Principle of Equivalence (the basis of Einstein's General Theory of Relativity) says that anyone can be a valid observer, but that the equations of motion may have to be adjusted to introduce imaginary (non-physical) forces.

    In particular, a non-inertial observer may invent imaginary forces so that Newton's first law is true.

    For example, a rotating observer invents an imaginary centrifugal force to explain why objects appear to move round him. :smile:
  10. Jun 27, 2008 #9


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    Re: non-inertial observer

    What if the inertial observer is a person holding a string while twirling an object around? I'm sure that person is going to feel the outwards tension force that is the result of the equal and opposite reactive centrifugal force of the object. The object "feels" the centripetal force from the string causing it to accelerate inwards. The string "feels" the reactive centrifugal force from the object at one end, and the centripetal force from the inertial observer at the other end, and experiences these opposing forces as tension.
  11. Jun 27, 2008 #10


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    Hi Jeff! :smile:

    Yes, that's why I emphasised "on an object moving in a circular path".

    An inertial observer recognises no centrifugal force on the object, but usually does recognise a centrifugal force from the object, on whatever is keeping it in the circle. :smile:
  12. Jun 27, 2008 #11
    A centrifugal force does not exist. The reason people think it does is because, say you are in a car that is turning right. You get pushed outward. They think this means that there is a force pushing you outward.

    That is completely wrong, it is actually the opposite that is true. A force is pulling you inwards. Think of a car accelerating in a straight line. You get pushed back in your seat; does this mean that there is a force pushing you backwards? Of course not, it is jsut the force of the car pushing you forwards (or to the center during a turn) and your bodies resistance to the change in motion.
  13. Jun 27, 2008 #12
    Your post sounds overly forceful (no pun intended) and more or less repeats several of the posts above. With that said, I would like to somewhat disagree with you.

    The centrifugal force is usual called a fictious/inertial/psudo/quasi force. The reason is simply because it is not an actual force in the Newtonian/formal sense. So really, it does exist, just remember to add fictious/inertial/psudo/quasi/etc before the word force.

    Regarding the accelerating car in a straight line, you being "pushed back" is just another example of a fictious force. Saying these effects do not occur can get you into some serious trouble. Not accounting for the centrifugal force can cause an intercontinental ballistic missile to hit your ally rather than your enemy.
  14. Jun 27, 2008 #13

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    Realize that two different meanings of "centrifugal force" are being discussed in this thread.
    • Using the "old-fashioned" meaning where centrifugal force refers to the 3rd-law pair ("reaction") of the centripetal force, then centrifugal force is quite "real" (it has an agent).
    • Using the "modern" meaning of centrifugal force as a psuedoforce, then centrifugal force only exists as an artifact of viewing things in a non-inertial frame. It's not a "real" force in that it has no agent.
    As tiny-tim points out, the two "centrifugal forces" act on different bodies. Most standard physics textbooks use the "modern" definition.
  15. Jun 27, 2008 #14
    guess I was never taught the old fashioned method. :(
  16. Jun 27, 2008 #15


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    What you feel is getting "pushed" inwards, doesn't matter if it's in a turn or linear acceleration. However, if there's someone sliding into you from the "inside" part of the seat, the "centrifugal force" from that person sliding into you is going to "feel" real.

    If an ice-skater were to spin around while holding weights, the skater could "feel" the centrifugal force. The force is only "ficticious" in that it doesn't result in acceleration of an object, but is the reaction force to acceleration.
  17. Jun 27, 2008 #16
    This is a better example! The only force constraining the skater's weights to move circular is applied to the weights by the skater's arms. Its the centripetal, and is the only force required to explain the weights motion.

    The reaction force is felt, as if the weights were being tugged outward. The human experience of forces is so conditioned that there is intuitive surprise in many that when the mass is released, the trajectory is a tangent!

    There is nothing wrong in language and culture about inventing an expression for this. Its not required for the calculation of the motion, but is necessary and relevant to express the experience of this reaction, whether it be "sliding across a seat" or "skaters spinning". To thump the tub as in "this force does not exist" is maybe to misunderstand its concept and purpose in language.
  18. Jun 27, 2008 #17
    That is incorrect. Something like that exists as soon as you define it. What your professor was referring to was the notion that the centrifugal force is what is known as an inertial force. Such forces can be transformed away be moving to an inertial frame of referene.

  19. Jun 28, 2008 #18


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    feeling the centrifugal force

    Our perceptions are designed to work in an inertial (non-rotating) frame.

    In a non-inertial frame, we therefore perceive things which are not really there.

    However, we really do perceive them! :smile:

    In that sense, although we see hear or feel things which are not there, we genuinely see hear or feel them.

    An observer holding onto a string which is whirling him in a circle feels a force along his arm toward the centre of the circle.

    However, he is "programmed" to work in an inertial frame.

    And he knows that he is not moving toward the centre.

    So he also feels a force in the opposite direction, balancing the force along his arm.

    In that sense, he genuinely feels a centrifugal force. :smile:
  20. Jun 28, 2008 #19
    Well Pete, no offense, but you weren't in the class room with me that day (or were you?), so how do you know what my professor was referring to? The science community for as long as I can remember has been consistent with my professor.

    I fully understand what you and others are referring to with the concept of "inertial force". The "forces" I'm referring to are those acting on a body in circular motion. My mechanical engineering dynamics profs, civil engr statics profs, and physics profs insisted that we draw free body diagrams detailing each and every force acting on the body in question. In these free body diagrams, "centrifugal force" does not show up anywhere. The velocity of the object is tangential, and the acceleration is centripetal, or inward. There is no outward force/acceleration, aka "centrifugal". If the object's linear speed is increasing as well, then another component of acceleration exists in the tangential direction.

    I understand what others have state about "inertial force". If I twirl an onject attached to a rope, I feel an outward force on my hand from the rope. That is merely tension. If I pull on a rope attached to an object, the object accelerates in the direction of my force. But I "feel" a "force" in the opposite direction due to tension. Call this "inertial" or whatever, but I do not accelerate in the direction of said force. Likewise with centrifugal "force". I feel it in the rope, but it does not accelerate me.

    The free body diagrams never include centrifugal force. If F=ma holds, then centrifugal would result in acceleration outward. It doesn't.

    I stand by what I wrote initially. As far as "something like that exists as soon as you define it" goes, I am at a loss. Does the mere fact that I define something, give it actual existance? I think that is quite a stretch. Peace and best regards.

  21. Jun 28, 2008 #20
    This is only true for the inertial observer. Consider, as I have used above, the example of a passenger (the non-inertial observer) in a car in uniform circular motion. To highlight the argument, let the car have no windows so the passanger is closed off from the rest of the world.

    In the case of the inertial observer,
    [tex]\Sigma F=-\frac{mv^2}{r}[/tex]
    where the negative sign indicates acceleration towards the origin (uniform circular motion).

    However, the non-inertial observer, where his only reference frame is the car, will say that
    [tex]\Sigma F=0[/tex].
    The reasoning here is that the centrifugal force is balanced by the normal force of the car pushing back into the passenger. So from the reference frame of the passenger, the free-body diagram will include the centrifugal force.

    This is precisely how one may simulate gravity on a spaceship....
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