Newton's first law says: In the absence of a force: A body at
rest will remain at rest. A body in motion will remain in uniform
motion.
A special case of this law can be stated: In the absence of a force: A body not rotating will remain in a fixed orientation. A body
rotating will continue to rotate at a constant rate.
Based on this law the earth will continue to rotate forever, unless a
force is applied to stop it. (bad news, there a drag force due to solar
radiation. So the earth's rotation is gradually slowing down.)
More important to us is that an airplane will not suddenly change attitude
unless a force is applied. On the other hand Newton also tells us that
once a rotation (roll, pitch, or yaw) is begun it won't stop unless a
force is applied.
One of the amusing debates that often goes on between pilots is about
what "makes an airplane turn?" Pilots argue about whether the
elevators or the fin "cause the turn." We will discuss this
in detail in the chapter on control, but right now you can see that strictly
speaking the answer must be neither. Assuming that the pilots are
debating about a steady turn (constant rate of rotation) then Newton's
first law tells us that there can be NO NET FORCE during the turn. I.E.
the airplane is turning for the same reason the earth is turning. So,
the only appropriate debate is about what starts a turn, and what stops a turn. The in between requires no force.
Moments and the Center of Gravity
To make an object move you can push on it anywhere. But, to make it rotate
there is ONE place you cannot push.
The one place is called the center of gravity.
In the teeter totter to the left the fulcrum point is exactly
at the center of gravity (circle with two red quadrants.) Therefore
the fulcrum applies NO TURNING MOMENT to the teeter totter board.
You can grab the board with your mouse and stop it at ANY ANGLE
- try and see. You can also "toss" the board. Once it
starts rotating it is just like the earth, it keeps rotating
forever. In this case it bounces off the ground and reverses
direction, but still it will rotates back and forth forever. This
is a "perfect" teeter totter, meaning that there is no
friction.
One of the most important things for you to see is that you can "balance" the teeter totter at ANY angle,
not just when level. Be sure to stop it at many different angles to convince yourself of this.
Real teeter tooters are usually built like the one to the left.
The center of gravity of this teeter totter is above the fulcrum
point.
Remember that the force is applied at the fulcrum, so in this case
if you tip the teeter totter even slightly it will "fall over"
and stay there. Try it and see. (You should notice
that the teeter totter doesn't just rotate, it accelerates.)
Notice that you can only balance this teeter totter when the center
of gravity (circle with two red quadrants) is directly above the
fulcrum. Any other position and the teeter totters.
To understand the physics of rotation you should completely forget
about the body in question. Think only about its center of gravity.
This is true whether thinking about a teeter totter, or an airplane.
The picture to the left shows the center of gravity of the first
teeter totter above resting exactly at the fulcrum point.
The blue vector is the force being applied by the fulcrum to the
teeter totter board. We could also have drawn in the weight vector
for the board - in this case I chose to draw the blue vector, which
in accordance with Newton's third law is the reaction to the weight.
The important thing to note is that the force vector passes exactly
through the center of gravity.
Whenever a force passes exactly through the center of gravity there
is no effect on the objects rotation. I.E. if it is not currently
rotating it will not start to rotate, or if it is currently rotating
the rate of rotation will not change. We say that there is NO ROTATIONAL MOMENT.
The picture to the left shows the center of gravity of the second
teeter totter as it would be if the board were rotated to the left.
This teeter totter is designed so that the center of gravity is
above the fulcrum point. As a result, when the teeter totter rotates
the center of gravity moves to the side of the fulcrum. The picture
to the left shows the situation where the teeter totter has been
rotated counter clockwise.
In this case the force from the fulcrum, which is always straight
up (since it is a reaction to the weight of the board, and weight
always acts toward the center of the earth) no longer passes through
the center of gravity. There is an ARM, which is just a fancy word
for the distance between the force and the center of gravity.
Note: there is no significance to where I drew the arm in the
diagram. It is better to think of it between the center of gravity
symbol and the force vector, but the diagram would have been too
cluttered if I drew it there.
Moment = Force x ARM
The above formula is an important one. More important is that you understand
the concept of moments. The two aspects you should spend time reflecting
on are:
If rotation rate is constant there is NO MOMENT
In order to have a moment there must be an ARM
The airplane to the left obeys the laws of rotation ( as does
a real airplane.)
However, unlike a real airplane it is flying in a vacuum, like
the space shuttle when in space.
Grab the airplane by the tail and rotate it. You can stop it at
any attitude and it will stay there.
If you start it rotating and let go it will keep rotating forever.
The picture to the left shows the same airplane but viewed from
the top. As with the one above you can turn it to any orientation
and it will stay there. Of, you can start it turning and let go.
You should be starting to ask yourself questions like:
When I pull back on the controls the nose goes up, but WHY DOES
IT STOP when I let go of the controls.
When I step on the rudder the airplane starts to yaw, but WHY
DOES IT STOP when I let go of the rudder
We don 't often think to ask such questions, because we are so
used to not thinking of the situation demonstrated in these simulations
as "real." But, this is how the laws of physics really
work. So, if you see an object stop rotating then there must
be a moment (force with an arm) that stops it.
We are just about ready to roll up our sleeves and start answering
some questions about why airplanes fly the way they do.
