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? The Ang. Speed = 7.29*10^-5 rad/s

1b) 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*10^3 km.

1c) What is the acceleration of the object on the surface of the earth in the previous problem?

Answer 1

1) Angular speed is angle / time

Full revolution means 2? radian or 360 degree.
Time = 23 hours 56 minutes and 4 seconds = 82800 + 3360 +4 = 86164 s

Angular speed = 2? radian / 86164 s or 360 / 86164 s

= 0.0000729 radian /s or 0.004178 degree /second
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2)
Linear speed = r ? where ? is the angular speed. Where ? is rad/s
v = 0.0000729*6.37

Answer 2

radius there = R sin theta = 5773 km

linear velocity = 5773*1000*ang vel

= 420 m/s

acceleration = v^2 / R = 0.030 m/s