Material:
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- A piece of 3/4" outside diameter PVC tubing (schedule 40)
- A hacksaw or tube cutter
- Colored pens (Non-permanent)
- A smooth surface such as a table top.
- (Optional: A transparent surface.)
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| Directions: |
- Clean all markings off tubing. (PVC cleaner
works well) Cut the tubing until its length is three times its diameter
(Err on the long side, this experiment will still work with tubes up
to 3.15 diameters long.) Mark and X on the side of one end of the rod
and an O on the other.
- After the first experiment you will want
a few more pieces of tubing. Cut them so that you have a set of tubes
with lengths that are 2,3,4, and 5 times their diameters.
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- Place your finger on the "X," push
the finger down as you pull it toward you. This will make the cylinder
spin and rotate at the same time. The cylinder will spin and rotate
making a blurred circle in which three X's can be seen. Notice that
the spinning cylinder stabilizes so that the X appears at the vertices
of a triangle. Notice the O does not appear. Press your finger down
rapidly to make the cylinder spin. Next place your finger on the O and
spin the rod. Notice that the O forms a triangle while the X does not
appear.
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| Safety Concerns: |
- None.
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| Questions: |
- Do experiments to figure out what is going
on. (Use overhead markers so students can change colors and designs.)
Make several markings on one end. Look at the spinning rod from underneath
through a transparent table. Look at the spinning rod in sunlight (which
does not strobe on and off like fluorescent lights.) Look at the spinning
rod with a stroboscope. A hand made stroboscope in which slits are cut
into the edges of a spinning disk will work just fine. (See the stroboscope
activity.) Draw a line down the side of the cylinder make one half of
the line red and the other half blue. Try cylinders of different lengths.
Notice the different stable patterns.
- Notice that the center of the spinning cylinder
is above the table, the cylinder rotates with one end in contact with
the table surface. Have students create challenges for other groups
of students, or write their challenge on the board.
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| Concepts: |
- When you launch the rod it spins about its
long axis and rotates about a line perpendicular to this axis.
As it rotates about its center, the rod forms a blurry circle on the
table top. As the rod spins, the top of one end moves in the same direction
as the end is rotating while the top of the other end moves opposite
the rotation. The arrows on the cylinder show how it move (the
entire top is moving down). The arrows off of the cylinder show
how it rotates. On the right end the two motions cancel, and the
top center comes to rest (momentarily); on the left end they add.
- The marking on the end that is moving opposite
to the rotation slows down, for each pattern of marks. For example in
the triangular pattern, there is one place on the cylinder where the
mark will come briefly to a complete stop. The marking on the other
end is going doubly fast. Human eyes can see the stopped marking easily
while the extra-fast moving mark is a blur. Thus, only the markings
on one end are visible.
- Since we see 3 markings around the blurred
circle we know that the cylinder is making 3 spins for every rotation.
Cylinders that are cut so that their length is four diameters have a
stable square with 4 markings, those cut to 2 diameters create a stable
pattern of 2 marks. At first with the tube that is 3 diameters
long the marks on one end appear but they do not form a stable pattern.
After a few seconds however, the marks settle into a stable triangular
pattern which persists until the cylinder slows to a stop. Notice also
that the cylinder spins and rotates with one end in the air.
- The key to understanding the behavior of
the cylinder is to realize that the cylinder makes a stable pattern
when the end touching the table rolls without slipping. Usually
the cylinder is launched so that it is spinning faster than it is rotating.
This means that the end touching the table rubs against the table, dissipating
energy and slowing down until it reaches a speed where the end of the
cylinder rolls without slipping. This is why the pattern is not stable
at first, but then stabilizes.
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