It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution

Question

It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution (mean sidereal day). What is the angular speed of the earth? Assume the earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the earth to the object makes an angle of 65.0° with the axis of rotation. The radius of the earth is 6.37×103 km. What is the acceleration of the object on the surface of the earth in the previous problem?

Explanation / Answer

angular speed = 2pi / T

w = 2pi / ( (23 x 3600 sec) + (56 x60 sec) + (4 sec)) = 2pi / ( 86164)

w = 7.29 x 10^-5 rad/s

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radius of person moving r = Rsin65 = (6.37 x 10^3 x 10^3 m ) sin65

r = 5.77 x 10^6 m

v = w r = (7.29 x 10^-5 ) x (5.77 x 10^6 ) = 420.86 m/s

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a = w^2 r = (7.29 x 10^-5 )^2 ( 5.77 x 10^6) = 0.0307 m/s^2

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