Well, if you get a few million miles above the north pole and look down, the earth spins counterclockwise about its axis and also orbits counterclockwise around the sun, so take that as positive,clockwise looking up :) (sun rises in the east :)
so daily spin:
2 pi rad/24 h * 1 h/3600s
= 7.27 *10^-5 rad/s
and yearly orbit:
2 pi rad/365.25 d
= .017202 rad/day but how many seconds in a day?
24 h * 3600 s/h = 86,400 s/d
so
.017202/86400= 1.99*10^-7 rad/s
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 direction for the angular displacement to be the direction of the earth's motion.
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