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chapter 8 problem 03 Chapter 08, Problem 03 The earth spins on its axis once a...

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 earths motion. (a) Number (b) Number Units Units

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
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Part\:a:

Average\:angular\:velocity\:is\:defined\:as:

\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

substituting\:and\:solving:

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

Part\:b:

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

substituting\:and\:solving:

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

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