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The earth spins on its axis once a day and orbits the sun once a year...

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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Answer #1

a)

Period

T=1 day =1*24*60*60 =86400 s

angular velocity

W=2pi/T =2pi/(86400)

W=7.2722*10-5 rad/s

b)

Period

T=365 1/4 day =365.25 day

T=365.25*24*60*60

T=3.15576*107 days

angular velocity

W=2pi/T =2pi/(3.15576*107)

W=1.991*10-7 rad/s

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