Question

(a) What is the angular speed ω about the polar axis of a point on Earth's surface at a latitude of 55° N? (Earth rotates about that axis.) (b) What is the linear speed v of the point? What are (c) ω and (d) v for a point at the equator? (Note: Earth radius equals 6370 km and let one day be 24 hours)

Answer 1

Answer

given,

radius of earth = 6370 km

earths latitude = 55° N

time  = 24 hour = 86400 s

angular speed = ω

a) $\omega = \dfrac{2\pi}{T}$

$\omega = \dfrac{2\pi}{86400}$

$\omega = 7.27 \times 10^{-5}rad/s$

b) $v = r\omega cos\theta$

$v = 6370\times 7.27 \times 10^{-5}\times cos 55^0$

$v = 266 m/s$

c) ω at equator

$\omega = \dfrac{2\pi}{T}$

$\omega = \dfrac{2\pi}{86400}$

$\omega = 7.27 \times 10^{-5}rad/s$

d) $v = r\omega cos\theta$

$v = 6370\times 7.27 \times 10^{-5}\times cos 0^0$

$v = 463 m/s$