A few points on this thread which started on moment of
inertia and has moved on to work and contact forces.
(1) Let's take care not to confuse zero net force and
absence of motion. The position of your center of mass will
change without any net force if you are already in motion.
(2) There is a single contact force between an object and
the surface with which it is in contact. It is often useful
to look separately at the component of the contact force
normal to the surface (often called the normal force) and
that parallel to the surface (the frictional force). However
it can be confusing to students if we reserve the term
contact force for the normal component.
That normal force is often referred to as the reaction
force, a pedagogically dangerous practice I believe to be
both an outcome and a source of misconception involving
Newton's third law.
(3) Brian Whatcott has reminded us that the motion of the
center of mass can be changed by having a net non-zero force
normal to the surface. He cites the example of an
astronaut; other examples are pushing down hard on a floor
or pushing away from a smooth wall.
Earlier contributions to the thread had ignored such
maneuvers because of concentration on the outcome of zero
frictional force. I think this is a nice example of the way
we concentrate on a particular aspect and ignore those
things we consider extraneous. This can confuse students.
Here our restriction was that we were confining ourselves to
forces parallel to the surface. If we make such a
restriction explicit then no harm is done. When the
restriction is implicit (as it was in this thread) we can
say (teach) things which may be correct in the restricted
sense we are thinking about but not in the wider sense that
some of our students are thinking about. In a situation
like the one we've been discussing, they come away believing
that if there is no friction, motion cannot be generated!
(4) Bob Carlson presented a number of examples to show that
a frictional force can do positive work. These are good
counter examples to a common misconception that friction
forces do only negative work (as when they stop motion).
There is an excellent argument that no work is done when
frictional force act to stop motion because the points of
contact between the object and the surface where cold
welding and shearing occur are localized. I won't pursue
that argument further here.
(5) Bob's examples are interesting but a question I would
like to ask is what is the point of calculating work at all?
Surely the important item is not whether work is done or how
much is done but what are the changes in energy and what
mechanisms are involved in those changes.
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.
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.
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.