University of Illinois, Urbana ChampaignTAM 212worksheet_11

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1. The way we have chosen the coordinate axes, the earth rotates about the y-axis with constant angular velocity ~! = !|^, where ! > 0. What are the numerical values of ! in rev/min and rad/s? 2. As... the earth rotates about the y-axis, your trajectory (in the reference frame of the earth) is a circle of radius r. Label the center C of this circle, as well as the distance r, in Figure 1 3. Recall that the acceleration ~a of an object moving in a circle of radius r with constant angular velocity ! points toward the center of the circle (i.e., it is centripetal). Draw your acceleration ~a in Figure 1 at the instant shown, placing the tail of the vector at your position. Below, express ~a in terms of ! and r in the given Cartesian basis 4. Label the radius of the earth RE and your latitude φ in Figure 1. Below, express r in terms of RE and φ. Use your answer to express ~a from Question 3 in terms of !, RE, and φ. [Show More]

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