Question

chapter 8 problem 03

Chapter 08, Problem 03 The earth spins on its axis once a day and orbits the sun once a year (365 1/4 days). Determine the average angular velocity (in rad/s) of the earth as it (a) spins on its axis and (b) orbits the sun. In each case, take the positive diretion for the angular displacement to be the direction of the earth's motion. (a) Number (b) Number Units Units

Answer 1

$\omega =\frac{\Delta \theta }{\Delta t}$

$\theta =angular\:displacement=2\pi \:rad\:\left ( Earth\:as\:a\:sphere \right )$

$t=time=1\:day=24\:hours\left ( \frac{3600\:s}{1\:hour} \right )=86400\:s$

${\color{Blue} \omega =7.27\times 10^{-5}\:\frac{rad}{s}}$

$t=\left (365\:\frac{1}{4}\:days \right )\left ( \frac{24\:h}{1\:day} \right )\left ( \frac{3600\:s}{1\:h} \right )=31,557,600\:s$

${\color{Blue} \omega =1.99\times 10^{-7}\:\frac{rad}{s}}$