Re: physical pendulums

[Bob Sciamanda <trebor@VELOCITY.NET>]

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.)

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).