Re: Constraint and inertia

[Gary Karshner <karshner@STMARYTX.EDU>]

> I'm not quite sure what is meant by the "coefficient of inertia," but I will
> assume that it is the coefficient for the difference between gravitational
> mass and inertial mass.  Tipler, Physics for Scientists and Engineers, Third
> Edition, states, "Their equivalence is now established to about 1 part in
> 10^12."  Tipler also states that Newton, "was able to establish the
> equivalence between gravitational and inertial mass to an accuracy of about 1
> part in 1000."

        If memory serves Newton established the equivalency of gravitational  and
inertial masses using an experiment of Galileo's where he made a pendulum
with a hollow head. Galileo did it to show that the period of a pendulum is
independent of the mass, but Newton realized that it also showed the mass
equivalency since to solve for the pendulum's motion one sets the
gravitational force on the mass equal to the inertial force of the second
law and the mass drops out only if the two types of mass are equivalent.
What amazes me the most about this experiment is that Newton saw the
problem and realized that this experiment shows the equivalency.
        The modern experiment is due to Etvos and uses a torsion pendulum with
different substances on each arm. This pendulum is effects by both the
earth's gravity and if I dare use the term the centripetal force caused the
earth's rotation. No deflection is observed so the masses of each of the
substances must be the same gravitationally and inertially. Dicke redid the
experiment in the 1960's. This months Physics Today has a picture that
looks like the three mass head used in the apparatus, but I don't have it
here and didn't read the article, so it may not be relevant. I am sure some
one on this list will correct me in either case.
        One last comment for those of you who are trying to follow this discussion
and are confused by terms used. The inertial mass is the mass that is due
to motion as described in Newton's first law whereas the gravitational mass
is what gravity pulls on. Why these should be the same thing is what led
Einstein to develop general relativity.

Gary

Gary Karshner

St. Mary's University
San Antonio, Texas
KARSHNER@STMARYTX.EDU