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Re: Centrifugal Force

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  • Re: Centrifugal Force


    the centrifugal force is a particular type of inertial force. It is well
    known that intertial forces are not real forces. They don't exist, according
    to Newton's definition of force, i.e. something able to produce an
    acceleration observed within an inertial reference frame. It seems weird,
    but you
    might say that "inertial" forces do not exist in "inertial" frames.

    A centrifugal force seems to exist, even though it doesn't, if you
    attach your reference frame to an object rotating about a fixed axis. In
    a rotating reference frame, called "non-inertial", your object appears
    motionless, and its
    acceleration appears to be null.

    However, you can measure a real force, i.e. the
    centripetal force, acting on the object and keeping its center of mass along
    circular trajectory. You can also deduce that an equal and opposite force
    exists, acting
    on the external environment (e.g. to a
    rope holding the object along its circular trajectory), and exerted by the
    object as a reaction to the
    centripetal force. This is a true force, and it is not what's called a
    "centrifugal" force (although its direction is radial and centrifugal),
    because it is applied to the environment, rather than to the object.

    Now you have a problem: you can measure a net force acting on the
    object, yet you see no acceleration. That's against Newton's first and
    second laws. Well, you have two ways to solve the problem:
    1) you realize Newton's laws are useless within a non-inertial frame (as
    Newton himself clearly specified);
    2) you introduce a force which really doesn't exist, which is acting on
    the object, and makes equal to zero the net force acting on the object
    itself. This is what's called the "centrifugal" force. Thus, you make the
    net force equal to the observed acceleration (both null). And you can use
    something which seems like Newton's second law (F=m*a) to explain the
    observed motion.

    In my opinion, Newton wouldn't agree to the second solution, because he
    had an hard time trying to explain to other people that a force (the
    centripetal force) is needed to keep an object along a circular or curve
    trajectory. That's how he could explain the elliptical motion of the planets
    and moon, and introduce the concept of gravitational force.

    Imagine how hard was for Newton (and even Galileo before him) to explain
    his ideas to
    those saying: "even though we can't be sure the earth is motionless,
    certainly it doesn't accelerate, because otherwise everybody would feel its
    acceleration". Well, this is exactly the
    point of view of somebody using a non-inertial frame. In this case, it is a
    reference frame attached to the earth, and since the earth is accelerating,
    that reference frame is not inertial. Using a non-inertial reference frame
    is a human natural habit. On this standpoint, Newtonian physics is not a
    natural way of thinking. In turn, those who like the natural approach should
    know that this is opposite to the Newtonian way of understanding nature.

    For instance, if you like to use a reference frame attached to your car,
    when your car is moving along a curve, you should know that this is a
    natural and easy way of thinking but it's not a Newtonian way of thinking.

    Of course, you need intelligence to understand
    the point of view of a theoretical observer which doesn't move relative to
    the fixed stars (and that would be the inertial reference frame). And that's
    why Newton's laws were discovered by Newton and not by Aristoteles, or
    Archimedes, or Pitagora, or some other ancient phylosopher or mathematician.

    Thus, if you want to teach basic mechanics and you want to be
    understood, I strongly suggest you not to use inertial forces, and highlight
    the need to use inertial frames, where you don't need such forces.

    You might ask why many high-level researchers still use inertial forces
    (and even inertial couples) in their studies, published in top-level
    refereed journals. The reason is that they prefer using non-inertial frames,
    where they can more easily describe the motion of some objects. For
    instance, if you use a non-inertial reference frame, attached to the thigh
    of a subject, you can easily describe the behaviour of the knee joint, and
    the motion of the shank relative to the thigh.

    Consider that the results of calculations performed within non-inertial
    frames are perfectly correct, equivalent to those you would obtain using
    Newton's laws and inertial frames.

    Consider also that there are other researchers (and I am one of those)
    which follow Newton's approach, and never use non-inertial frames. Of
    course, everything can be done that way, although others might say that the
    motion of multi-body systems such as the human body is easier to analyze
    using non-inertial frames. So, there's no need to introduce inertial forces
    such as the centrifugal force in this case, but then again,
    the final results of any calculations are perfectly equivalent to those
    obtained by researchers using inertial forces within non-inertial frames.

    The use of inertial forces (such as the centrifugal force) within
    non-inertial frames is called the D'Alembert's approach. The use of inertial
    frames is obviously called classic mechanics, or Newtonian

    In the past, there have been a few real interesting discussions about
    this theme on BIOMCH-L. If you are interested, you might search in the
    BIOMCH-L database.

    With my kindest regards,

    Paolo de LEVA

    University Institute of Motor Sciences
    Biomechanics Laboratory
    P. Lauro De Bosis, 6
    00194 ROME - ITALY

    Telephone: (39) 06.367.33.522
    FAX/AM: (39) 06.367.33.517
    FAX: (39)


    Tel./FAX/AM: (39) 06.336.10.218

    ----- Original Message -----
    From: "Gary Christopher"
    Sent: Monday, December 11, 2000 3:31 PM
    Subject: Centrifugal Force

    In teaching and studying Biomechanics I have used three textbooks, all of
    which mention, and then try to justify, the existence of centrifugal force.
    Yet if I check my physics book it tells me flat out that there is no such
    thing. What is the biomechanics community's take on the subject?

    Just so you know my personal leanings, I don't put any stock in its
    existence, so I'm left trying to convince my students why I'm right and
    their textbook is wrong.

    If we all believe Newton's Second Law of Motion, we should be able to easily
    determine that the so-called "centrifugal force" is, in fact, fantasy. If we
    believe Newton's Second Law, we should scoff at the notion of a force that
    does not have an accompanying acceleration.

    As is customary, I will post a summary of responses. Please reply directly
    to my email:

    Gary Christopher
    Brigham Young University

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