Why is it easier to balance a bowl on a finger when is is placed on
the finger upside down( when the rims are down) than it is when the
bowl is on your finger properly? I AM LOOKING FOR AS SCIENTIFIC AS
POSSIBLE EXPLANATION!!

Dear plmokn-ga;

Thank you for allowing me to answer your interesting question. Simply
put, the matter is relative to the state of equilibrium. Stable
equilibrium is an equilibrium that is restored if disrupted by an
external force; in this case gravity.

Imagine that you had a ball inside a bowl; if the bowl is not
disturbed the ball will rest at the lowest center of gravity in the
bottom of the bowl. Now turn the bowl over and put the ball on top of
the highest point on the bowl. Equilibrium here is unstable and unless
the ball is very carefully placed it will not rest in a motionless
state. Gravity pulls at the weakest point and the ball tends to roll
off the bowl.

The same is true if you finger replaces the ball. Place the bottom of
the bowl on the tip of your finger and try to balance the bowl. It is
quite difficult because the state of equilibrium is unstable. Now
invert the bowl so that your finger is in the center of the inside of
the bowl. The bowl balances well because the state of equilibrium is
stable.

Take a look at this graphic:

LECTURE SCREENS
http://www.atmos.ucla.edu/AS3/scrns/top11/Note09.html

Imagine the ball and bowl scenarios in the graphic. Here the ball is
balancing on the bowl.

Now imagine that the location of the ball is the tip of your finger.
Here the bowl is balancing on the ball (your fingertip) so the concept
is reversed but the fundamental rules remain the same.

In short, the sides of the inverted bowl balanced on your fingertip
act like a tight-rope walker?s balance pole, stabilizing the
equilibrium and offsetting the balance inequities that occur when the
bowl is balanced upright on the fingertip.



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Best regards;
Tutuzdad-ga ? Google Answers Researcher



OTHER INFORMATION SOURCES

Motion on precribed trajectory
http://kr.cs.ait.ac.th/~radok/physics/b5.htm




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Request for Answer Clarification by plmokn-ga on 21 Aug 2004 15:21 PDT

Thank you for your answer. Upon review I realized that I didnt
understand it properly. At the end of the 3rd paragraph you wrote "The
bowl balances well because the state of equilibrium is stable." Why is
that so ? Why is the bowl more stable upside down? Thank you

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Clarification of Answer by tutuzdad-ga on 21 Aug 2004 15:59 PDT

The center point of balance is forced downward onto the tip of the
finger by the sides of the bowl (lower than the center point of
balance). Because the sides of the bowl are equal all the way around,
the equilibrium is stable.

Tie a button on the end of a string. Drape the string across the tip
of your finger. The string will slip off because the equilibrium is
unstable.

Tie a button on both ends of a string. Drape the string across the tip
of your finger. The string will balance (hang) because the equilibrium
is stable.

The same is so with a tightrope walker's balance pole. While the pole
seems straight, the ends actually droop down adding equal weight to
each side of the tightrop walker. This is why tightrope walkers use
such an extraoridinarily long pole and not a short one. He wants the
ends to droop down as far as possible to exert as much downward force
onto the center baland point (his feet) an posible so as to hold him
tighter against the rope and make his stable. The ends of the pole act
as weights in the same way that the buttons act as weights on the
string and the lower, equally distributed edges of the bowl act as
weights.

With the bowl upright, there is no way to redistribute falling weight.
In other words, when the upright bowl begins to shift (fall) a
catastrophic chain of events (force from gravity) that cannot be
countered it set into motion and causes the bowl to continue its fall.
With the bowl upside down and the equally distributed weight acting as
it's own counter-weight systemn, subtle compensation (just like the
tightrope walker does) can easily redistribute the weight when the
bowl favors one side or the other thus making the bowl teeter equally
in, what is literally, a balancing act.

tutuzdad-ga

Thank you!! Well done.

lower center of gravity

When the bowl is upsidedown:
 ____
/    \

Imagine that it tilts one way:
__
  \
   \
   |
Picture the center of gravity of the bowl, and then picture the
leverage that gravity has around that point (where your finger is).
The side that tilts up gains leverage, while the side that goes down
loses leverage, and gravity re-stabilized the bowl.
 ____
/    \
If the bowl is tilted up, when the bowl starts to tilt one way, the
side that goes down gains even more leverage, and the side going up
loses leverage, and the rotation of the bowl speeds up, and the bowl
falls.

\____/

In science we learned that the total weight of an object can be assumed as to be 

concentrated and passing through the object's center of gravity or
centroid. And gravity is

what causes this weight. And this weight points toward the center of
the earth, or just

plain vertically downwards. So think of the weight of the bowl as a
heavy arrow pointing

downwards vertically and passing through the bowl's centroid.

The centroid of the bowl is located above the base of the bowl,
somewhere in the hollow

space above the base. Also, the centroid is located along the axis of
symmetry, which is an

imaginary line passing through the center of the base of the bowl. This axis is 

perpendicular to the plane of the center of the bowl, so if the bowl
is balanced at its

base's center by your finger, then the weight of the bowl passes
through the tip of your

finger. Then the weight of the bowl is like sitting on your finger's
tip. The bowl just sit

there and in balance or equilibrium, or stable.

Now if you push slowly the lid of the bowl, the bowl will tend to tilt
in the direction of

your push. Once your push is strong enough to overcome the inertia of
rest of the bowl, the

bowl pivots on your finger tip and starts tilting. And so the axis of
symmetry will also
start tilting. And so the centroid will start leaving the vertical
line through your

finger's tip. And so the weight of the bowl, always passing through
the centroid and always

pointing vertically downwards, starts leaving the tip of your finger...

a) If the bowl is open upward:
....Your push tends to rotate the bowl about your finger tip. The
weight of the bowl will

also tend to rotate the bowl in the same direction of your push. Your
push and the weight

will help each other in toppling the bowl off your finger's tip in the
direction of your

push. Once the weight leaves your finger tip, there is no stopping the
bowl's tilting or

instability.

b) If the bowl is open downward:
....Your push tends to rotate the bowl about your finger tip. But
here, the weight of the

bowl will tend to rotate the bowl in the opposite direction of your
push. Remember that the

weight tends to rotate about the pivot or your finger tip. So here,
the weight will tend to

"fight" or "right" your push from toppling the bowl off your finger's
tip in the direction

of your push. Once the weight leaves your finger tip, the weight will
try to "right" the

overturning. Hence, you need a bigger push than in (a) above to
overcome this righting

moment of the weight. Therefore, here, you can say it is more "stable"
than in (a) above.

------------------
I could have explained it by using moments right away, but I don't
know if you would

understand moments.
Moment is force times perpendicular distance. It is like torque. It is
overturning moment or

turning moment about a point or about an axis. It is rigthing moment
if it is in the

opposite direction of the turning moments.

The short answer is :
it's hard to balance when the center of gravity is above the point of contact.
easy when below.

When the bowl is inverted tilting it requires energy (as stated
earlier, to lift its center of mass). When the bowl is right-side-up,
tilting it reduces its energy, which makes it unstable to tilting
(systems spontaneously move to minimize total energy)

It's the same reason that it's hard to balance a ruler on your finger
and easy to suspend a ruler, pendulum-like,  from between your
fingers.