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Paolo De Leva
12-12-2000, 02:21 AM
Gary,

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
such
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
its
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
mechanics/approach.

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) 06.36.00.31.99

Home:

Tel./FAX/AM: (39) 06.336.10.218

----- Original Message -----
From: "Gary Christopher"
To:
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: gac6@email.byu.edu

Gary Christopher
Brigham Young University

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