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About 500 years ago, when people were arguing that the earth went around the sun and that the earth that turned on its axis to produce day and night, some people objected that we would know if the earth were turning because we would feel it. Let's explore whether this might be the case.

a.) First let's think about what we can detect with our senses. Draw on your experience with motion to decide what it feels like to be moving with

• a constant velocity (as on a car, train, or plane)
• a constant acceleration (as in a long elevator at the beginning or end of the trip)
• a constant jerk, i.e., a uniformly changing acceleration (as in going over a bump or sharp hill in a car)

In each case describe whether or not you perceive such motion and in what ways. Be sure to describe experiences you have had that enable you to draw these conclusions. (The examples given are meant to be possibilities. You may choose other experiences.) Discuss in what way the sensations you experience of each of these kinds of motions would or would not allow you to detect (in principle) the rotation of the earth.

b.) In analyzing uniform circular motion, we were able to determine the magnitude of the acceleration and obtain the relation a = v²/r. (In calculus-based classes this is typically done by taking derivatives. In non-calculus-based classes it is typically done by comparing similar triangles containing the change in the position vector and the change in the velocity vector.) Use a similar argument to derive a formula for the magnitude of the rate of change of the acceleration (the jerk).

c.) Ignore the yearly motion of the earth around the sun and approximate the motion of the earth as that of a fixed sphere rotating on its axis. Estimate the magnitude of the velocity, acceleration, and jerk that you experience by participating in this uniform rotation.

d.) Compare the magnitude of the velocity, acceleration, and jerk that you calculated in part c.) with ones that you sense in you everyday life, such as riding in an airplane, going up in an elevator, or going over a bump in the road in a car. (To calculate these numbers you will also have to make some estimates.) Given these numbers and your answers to parts a.) and c.), if the earth were turning on its axis once a day, discuss whether would you expect to perceive the daily rotation of the earth.

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Page last modified November 2, 2007:R25