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Re: MOMENT OF INERTIA

On Mon, 21 Dec 1998, Brian McInnes wrote:

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.

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

I assume that you mean that the system is the person and the wall. In
that case I agree that no work is done.

I am interested in your use of the term "mechanism". To what does that
refer, and what insight does that give us in solving the problem. I don't
find that word used by Arons. But then, I have the 1990 edition.

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.

If the system includes the wall, then there is no outside force acting,
since the wall is part of the system. It seems that your use of the word
"system" and mine are not with the same meaning.

Secondly, although you deny that work is being done, you use the
calculation of work to determine the change in kinetic energy. How does
refusing to use the word make using the calculation okay? "A rose by any
other name . . ."

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.

Similar comments apply to the sliding box.

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?>

I have taken your friendly hint and reread the applicable portions of
Arons (pgs 115-140 in the 1990 edition). I should have done that before
my initial response a few days ago. I should be using the term
"pseudowork" when referring to displacements of the center of mass and
reserving the word "work" for the quantity in the First Law of
Thermodynamics as he suggests.

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.

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.

I interpret your reference to the contact force as meaning the force
normal to the surface of contact. Since that force is through the center
of rotation, it cannot be responsible for the torque that produces the
rotation.

Mervin Koehlinger
Physics Instructor
Concordia Lutheran High School
Fort Wayne, Indiana