For those who learn visually rather than algebraically (which often includes
me), try this. Sorry to use words to describe a picture, but if we step
through this one step at a time, and if I am successful in conveying the
picture, I promise it works and has repeatedly cleared up this issue in the
minds of many students (and profs).
(1) Draw a fairly large circle one a piece of paper. This represents the
path of the floor of the space station.
(2) Place a dot at the center of the circle. This represents the center of
the space station.
(3) Place a dot at the bottom of the circle. This represents the astronaut.
(4) Place a dot half-way between the astronaut and the center of the circle.
This represents the point where the ball is released. It is a bit extreme,
it means the radius of the space station is only twice the height the
astronaut can reach, but it is valid and serves our purpose.
(5) Imagine the station is rotating clockwise from our viewpoint. Draw a
vector to the left starting at the astronaut's feet and running tangential
to the circle at that point. This is represents the tangential velocity of
the astronauts feet.
(6) Draw a vector to the left starting at the ball-drop location. This
represents the tangential velocity of the ball at release. IMPORTANT: Draw
the length of the ball's tangential velocity only one-half as long as the
vector you drew for the astronaut's feet. This is the correct scale if the
ball release is half the radius of the feet.
(7) Now realize that the lengths of your vectors also represent the distance
the objects would travel in one unit of time. It does not matter what that
unit of time is. However, the ball's path will be straight, and the
astronaut's-feet path will be curved. We're going to draw successive
delta-position curves for the ball and for the feet.
(7a) Draw another vector for the ball, collinear with the first, and
starting at the arrow of the first. This second vector shows where the ball
will be at the end of the second time unit. Repeat this for the third time
interval, etc.
(7b) To see where the feet will be, draw a curved arrow starting at the dot
where the feet started, and follow the original circle you drew, but make
the curved arrow have the same length as the tangential-velocity vector you
originally drew for the feet. Then repeat this for the second unit of time,
etc.
(8) The straight line of the ball's path will intersect the curved line of
the feet's path, but the ball will clearly arrive at that intersection after
the feet have arrived.
* * * * *
You can repeat this for a ball thrown "upward" (toward the center of the
circle) from the feet. Now you have to initially draw two vectors for the
ball, one tangential and one radial. After doing that, draw the resultant
for the ball's velocity. Now extend this line for equal time units like in
the example above. In this case the ball's path clearly intersects the path
of the feet at a time before the feet get there.
* * * * *
Hence if you drop a ball, it lands "behind you" If you throw it "up", it
gets "ahead of you."
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817