Answer
(a) $\frac{\pi}{12}\ rad/hr$
(b) $0$
(c) $1676\ km/hr$
(d) $1185\ km/hr$
Work Step by Step
(a) The Earth revolves $2\pi$ radians in 24 hours, thus $\omega=\frac{2\pi}{24}=\frac{\pi}{12}\ rad/hr$
(b) At the North Pole or South Pole, $r=0$, we have the linear speed $v=r\omega=0$
(c) At Quito, Ecuador, a city on the equator, $r=6400\ km$, we have the linear speed $v=r\omega=6400\times\frac{\pi}{12}=\frac{1600\pi}{3}\approx1676\ km/hr$
(d) At Salem, Oregon (halfway from the equator to the North Pole), $r=\frac{6400}{\sqrt 2}\ km$, we have the linear speed $v=r\omega=\frac{6400}{\sqrt 2}\times\frac{\pi}{12}\approx1185\ km/hr$
