Re: MOMENT OF INERTIA

[Brian McInnes <bmcinnes@PNC.COM.AU>]

Reply to Mervin Koehlinger's comments


> Whether or not work must be taken into account and, for that
> matter,
> whether or not heat transfer must be taken into account depends
> upon your
> choice of system.  Both work and heat measure transfers of energy
> from one
> system to another.  By appropriate choice of system, one can limit
> consideration to only energy transformations, as you point out.
> However,
> there are problems where it is useful to so define the system that
> energy
> transfers are also present and, therefore, working and
heating must
> be
> considered.

I was careless in the way I used "transfer".  I agree with
your use of transfer for energy entering or leaving the
system and transformation for changes within the system.
But we can't have transfer if working and heating are both
zero: see later.

> > For Brian's astronaut launching from wherever in a
> > space-ship or a person pushing off a wall, there is an
> > energy transfer from chemical energy of the muscles to
> > kinetic energy of the center of mass.  The mechanism is the
> > normal contact force between the body and the surface.
>
> Careful.  We need a more precise definition of the system here.

The system I'm considering is the person pushing off the
wall.


> If your
> contact
> force is the force of the wall on the person, then there is an
> outside
> force acting and there is an energy transfer by working, not an
> anergy
> transformation.

I agree there is an outside force acting but I disagree
about the energy transfer.  The work done by the contact
force acting on the person is zero.  The hand does not move
during the time the normal force is applied to it.  So what
we have is a transformation of energy, not a transfer. The
center of mass has been displaced and the person has
acquired translational kinetic energy (at the expense of
chemical energy). We can calculate the kinetic energy by
integrating Newton's second law over the displacement of the
center of mass; this tells us that the product of the net
force (the push from the wall) and the displacement of the
center of mass is equal to the change in the kinetic energy
of the person.  This is superficially like the work-energy
relation for a particle but it is physically different.

> > For the box sliding to rest on a rough horizontal surface,
> > there is an energy transfer from kinetic energy of the box
> > to thermal energy of the system of box and surface.  The
> > mechanism is the frictional force between the box and the
> > rough surface.
>
> Again, what is the system?  If only the box, then friction is
> working.  We
> have energy transfer and energy transformation.

I have a major difficulty with taking the box alone as the
system for the consideration of energy changes.  Both the
box and the rough surface on which it is sliding get warmer
(increase their thermal energy); it is difficult to
calculate the energy transfer as heat from a box-system.
That is why I defined the system as box and surface.  I also
believe there is no work being done because of the forming
and shearing of junctions mean that again there is no
displacement of contact force.  In the box-surface system
there is neither work nor heat transfers but a
transformation. Again the change in kinetic energy of the
center of mass of the box can be quantified by going to the
box only system and using the fact that the product of the
net force (the frictional force opposing the motion) and the
displacement of the center of mass is equal to the change in
the kinetic energy.  All of this is treated with his usual
exquisite thoroughness by Arnold Arons on pages 137 to 144
of Part III of Teaching Introductory Physics.  (Are there
list members out there who haven't got or, at least, read
this book?>

> > For the hoop rolling down the incline (which is close to
> > where this thread started) there is a transfer of energy
> > from the gravitational potential energy of the system of
> > hoop and earth to translational and rotational kinetic
> > energy of the hoop.  The mechanisms are the gravitational
> > force between the hoop and the earth and the contact force
> > between the incline surface and the hoop.
>
> Ditto with regard to the gravitational-kinetic
transformation.  But
> how
> does the contact force come into play?  It is perpendicular to the
> motion.
> It can't be affecting the motion.

The contact force is a constraint force.  It doesn't do any
work but, together with the gravitational force, it
determines the motion.  First it stops the hoop from
falling. Second it supplies the torque that leads to the
rotation.  That's why I refer to it as (part of) the
mechanism for the process to occur.  The process gives us
the motion we observe and then, acting like accountants, we
can do our sums to finds how much energy is in each of the
different forms.

Brian McInnes