p11_027.pdf

27. (a) Earth makes one rotation per day and 1 d is (24 h)(3600 s / h) = 8 . 64

10 4 s, so the angular speed

ofEarth is

2 π rad

8 . 64

ω =

10 4 s

=7 . 27 × 10 − 5 rad / s .

(b) We use v = ωr ,where r is the radius ofits orbit. A point on Earth at a latitude of40 ◦ moves along

a circular path ofradius r = R cos 40 ◦ ,where R is the radius ofEarth (6 . 37

10 6 m). Therefore,

its speed is

v = ω ( R cos 40 ◦ )= 7 . 27

10 − 5 rad / s 6 . 37

10 6 m cos 40 ◦ = 355 m / s .

10 − 5 rad / s).

(d) The latitude is 0 ◦ and the speed is

v = ωR = 7 . 27

10 − 5 rad / s 6 . 37

10 6 m = 463 m / s .