Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 125: 40b

Answer

The linear speed at the North Pole or the South Pole is zero.

Work Step by Step

The earth rotates through an angle of $2\pi$ radians in 24 hours. We can find the angular speed: $\omega = \frac{2\pi~rad}{24~hrs}$ $\omega = \frac{\pi~rad}{12~hrs}$ $\omega = 0.2618~rad/hr$ The angular speed is $0.2618~rad/hr$ At the North Pole or the South Pole, the radius of rotation is zero. We can find the linear speed: $v = \omega ~r$ $v = (0.2618~rad/hr)(0)$ $v = 0$
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