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Re: physical pendulums

On Thu, 23 Sep 1999 10:42:03 -0400 Bob Sciamanda <trebor@VELOCITY.NET>
writes:
Hi Herb,
In your equation L = I/mh , I is the moment of inertia of the body
about an axis through the point of suspension. Thus, this "Center of
Oscillation" is not a single point in the body, it is defined only
relative to a given point of suspension. (Your fiqure of 2/3
assumes the point of suspension of the dowel is at one of its ends.)


You are correct concerning my assumption that the point of
suspension of a dowel-stick pendulum is at one end of the
stick. Our original problem was to compare such a swinging dowel
stick pendulum with that of a simple pendulum. I assxumed that
the point of suspension was at one end of the string of the simple
pendulum and at one ond of the dowel stick for the physical pendulum.

Herb




Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: Herbert H Gottlieb <herbgottlieb@JUNO.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, September 23, 1999 1:29 AM
Subject: Re: physical pendulums


On Wed, 22 Sep 1999 23:48:43 -0400 Bob Sciamanda
<trebor@VELOCITY.NET>
writes:
Herb, I think you are confoosed!

The center of oscillation (defined only with respect to a given
suspension point in the body) is that point which, when used as
the
point of
suspension, gives the same period of small amplitude
oscillations.
That is not the question asked.


Am I really confoosed ????

According to University Physics, 5th edition by Semat, Zemansky,
and
Young
(P205), "It is always possible to find an equivalent simple
pendulum
whose
period is equal to that of a physical pedulum." ...... "Thus, so
far as
its period
of vibration is concerned, the mass of a physical pendulum may be
considered
to be concentrated at a point whose distance from the pivot is
L=I/mh.
This point is called the CENTER OF OSCILLATION of the pendulum.

Herb

----- Original Message -----
From: Herbert H Gottlieb <herbgottlieb@JUNO.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Wednesday, September 22, 1999 11:15 PM
Subject: Re: physical pendulums


On Wed, 22 Sep 1999 19:30:53 -0700 fred brace
<fredb@TELEPORT.COM>
writes:
I am using a set of physical science lab materials on the
pendulum. One of the activities asks the students to get a
washer, a
bolt
and a long wooden dowel to swing with the same frequency. It
says
that if
the center of masses line up, then the pendulums will have the
same
frequency. Is this true?


Herb Replied:

> This is almost true, but not quite true. For a uniform wooden
dowel, the center of mass is at the center of the dowel.
It's "center of oscillation" is located at distance equal
to 2/3 of its length , measured from its point of suspension.
Thus a simple pendulum consisting of a uniform steel washer
at the end of a string of negligible mass would have the same
frequency as the swinging wooden dowel if the length
of the simple pendulum is 2/3 as long as the dowel. This is
explained in
detail in most of the popular physics books for introductory
physics.

Herb Gottlieb from New York City
(Where Professor Zemansky of our City College did a great job
explaining this in his College and University Physics
testbooks).