Life in a non-inertial frame

Frames of Reference: Playing ball in a non-inertial frame of reference - page 3

   We can show what happens by drawing, first, a series of diagrams based on what we know well -- the motion of the ball as viewed from a fixed frame of reference. We know that viewed in a fixed frame the motion of a ball thrown horizontally on a merry-go-round will travel in a straight line at uniform speed. If we view this motion looking down from above the merry-go-round, the ball will be seen moving in a straight line. From that point of view, the merry-go-round will appear to be rotating, and the person on it will move in a circle.

   To be able to truly ignore the effect of gravity on the moving ball, let us suppose we throw the ball not across a merry-go-round, but across a spaceship, far away from all gravitational forces. The spaceship is rotating, so as to produce artificial gravity for its occupants. It is more fun to do spaceship problems than merry-go-round problems anyway. We call these spaceship analysis problems, "Space Tracies."

Space Tracies: Let's work out the first one together

   Consider, as the first spaceship example, a ball thrown so that from the outside ("above") its direction of throw is directly across the spaceship. Suppose that a movie is made of the motion, with the interval between "frames" of the movie chosen so that, at the speed that the ball is thrown, the ball will reach the other side in exactly four frame intervals. (During each frame interval, the space ship rotates one eighth of the way around.)
   The diagrams in the left hand column of the Space Tracies picture at the right, show the five positions of the ball at these intervals, as seen from a fixed position "above" the spaceship. The diagrams show the ball beginning with the original position of the person throwing it to the other side.
   The speed of rotation of the spaceship is such that in exactly the same time, the spaceship makes a half turn counter-clockwise, so that just as the ball reaches the opposite side, the person who threw it has rotated around to the same spot and can catch the ball there.
   To show what this looks like to the person in the spaceship, each diagram of the left column is rotated the corresponding number of eighths of a complete circle, and the result is shown in the right column.
   To keep the person's position fixed, the diagram at the left must in each case be rotated in the direction opposite to the rotation of the spaceship the correct number of eighths of a complete rotation. The rotated diagrams leave the person always in the original position, the position that seems to her as her "fixed" position (in the rotating spaceship).
   In the rotated diagrams, we see the motion of the ball as it appears to the person, who is fixed at one location in the space ship.
   In the composite of the five pictures on the right one can see that, in a frame fixed in the rotating spaceship, the path of the ball, in the absence of all forces on it, is not a straight line, but a nearly circular path. This is because the motion is viewed in a non-inertial frame of reference. (Note, she must throw the ball to her left to accomplish this - see arrow.)

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