Life in a non-inertial frame

Frames of Reference: Playing ball in a non-inertial frame of reference - page 4

Several other "Space Tracies":

    At the right, and on the next page, are several more examples of "Space Tracies," in which the right hand column is left for you to do.

   In these examples, the rate of turning of the spaceship and the speed of the ball, are varied, to produce more intriguing outcomes. In the left hand column in each case we have filled in the views as seen by a fixed observer "above" the spaceship, for whom the path of the ball must be a straight line while the spaceship rotates counter-clockwise. In each picture of the right hand column, the spaceship has been rotated back, clockwise, to the position that leaves the person in her original position.

Recommended strategy for solving "Space Tracies."

   The recommended strategy for you is:
(1) In each drawing of the right hand column, place the dotted line as it would appear after the spaceship has been rotated the correct portion of a circle clockwise to just reverse the counter-clockwise rotation of the spaceship.
(2) Transpose the arrow on the dotted line along with the dotted line, so that the arrow in the dotted line in the right column shows the direction the ball is traveling, as seen in the rotated frame of reference.
(3) Place the ball on the dotted line, approximating a distance from the beginning of the dotted line along the direction shown by the arrow, that is the correct fraction in fourths, or eighths, of the entire distance across.
[In effect, you have now done the equivalent of cutting out the drawings in the left column, and rotating them until the peron's location is again the same as it was in the first drawing. In fact, if you find this difficult at first, you might try doing it just that way -- cutting out the sequence of drawings on the left, and pasting them, rotated, on the right. Be sure to label the pictures with the sequence number before you cut them out.]
(4) Finally, when you have shown where the ball is in each of the frames, as seen by the person on the spaceship, combine all the positions in the right hand column in a composite below. Number the positions, so you can keep track; then draw a smooth line in the composite indicating the path the ball will have taken as seen by the person on the spaceship, in the non-inertial frame of reference.

This exercise may persuade you that freely moving objects do not necessarily follow a straight line if observed in any frame of reference that is not inertial, i.e., that is accelerated. You can make up examples of your own, such as motion in an accelerating bus.

Have fun!

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