Multiple Sides of the Moon

Question:

If a person told you that they could easily prove that the
moon does not spin on its axis because, on Earth, we always
see the same face of the moon, what would you say?

Terminology

rotation - an object spinning around it's axis.
revolve - one object circling another.
center mass* - an objects geometrical center.
center gravity* - the center of an objects weight. 

* The earth's center of gravity and center of mass are at the
exact same location.  The moon, however, due to its oblong
shape, has a center of gravity separate from it's center of
mass.  The moon's weight is distributed in such a way that it's 
heavier side faces earth.

Fact #1

The moon does indeed rotate.  However, it rotates slowly,
about once every 28 days.

Fact #2

This rotational rate matches the rate at which the moon
revolves around the earth.

Fact #3

If the moon changed it's rate of rotation or revolution at
all, we on earth, would see all of it's faces.  It due to this
correlation between the moon's rotational and revolving rate,
that we always see the same side of the moon from earth. (see
Fig. 1)

Question:

What keeps the moon revolving and rotating in such a manner so that we always
see the same face.

Fact #4

The answer to this question has to do with the tendency for action to occur 
by way of expending the least amount of energy necessary.


 
Question:

How does this tendeny work to keep the moon spinning in perfect
alignment with the earth?

Fact #5

When the moon is aligned with the earths gravitational field in such a manner 
that it's heaviest side is facing earth, less total energy is in the system.

In Other Words:

The moons long axis must be aligned with the
"line" connecting the earth's and moon's center mass. That
line represents the earth's gravitational field.  If this was not the case, energy
would be expended unessesarily.

To Demonstrate

Materials: a minimum of three people, one three to five foot
piece of string 

Procedure:

Step one:  One person volunteer to represent our earth.  That
person will hold one end of the string at his or her "center
mass".

Step two:  A second person volunteer to represent our moon. 
That person will tie the other end of the string at his or her
left  wrist.  By keeping his wrist at a constant position the moon's 
center  of gravity will be represented at the point where the string 
meets his wrist.  This position should be directly infront of a location 
on the persons body that they will designate as their "center mass".   

Step Three:  One or more people volunteer to represent fixed
objects (stars, other planets), and observe the activity from
out side of the circumference of the moons revolutions around
the earth.
 
Step Four:  The "moon" will slowly begin to revolve around the
earth, keeping the sting attached to it's center gravity and
pulled tight.  By doing this, the moon will be pulled to face
the earth. As long as the moon's center mass and center gravity are
aligned with the earth's center mass this will hold true. You will
notice that by the time the
"moon" has revolved once, it has also rotated 
exactly one time.

Question:

What happens to this procedure when the moon revolves without
rotating?

Does the moon appear to be rotating from the perspective of
fixed objects (stars, other planets) outside of the moons
revolving circumference?