Rotation of sphere problem, acceleration and velocity

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The discussion revolves around calculating the angular speed, linear speed, and acceleration of an object on Earth's surface based on its rotation. The angular speed of Earth is confirmed as 7.29×10^-5 rad/s. A user attempts to calculate the linear speed using the formula V = r ω but encounters confusion regarding the use of 81400 in their calculations. It is clarified that the correct period for Earth's rotation is 23 hours 56 minutes and 4 seconds, which resolves the issue. The conversation emphasizes the importance of accurate values in physics calculations.
Staerke
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Homework Statement



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?
7.29×10-5 rad/s

(Got this one not too badly)

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 76.0° 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?

Homework Equations



V = r ω
a = v^2/r

The Attempt at a Solution



V = r ω
(sin(76)*6370000)*(2pi/81400) = 477 m/sec
a = v^2/r
(477.089)^2/(sin(76)*6370000) = .036826 m/s^2

Apparently these are wrong. Anyone how to get to an answer here?
 
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Where did the 81400 come from in your velocity formula?
 
gneill said:
Where did the 81400 come from in your velocity formula?
The period of the earth
 
Staerke said:
The period of the earth

Maybe you should check that figure. The rotation period (sidereal) is 23hr 56min 4sec.
 
That was my issue. Thanks for the reply :)
 

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