Rotation of sphere problem, acceleration and velocity

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Homework Help Overview

The discussion revolves around calculating the angular speed, linear speed, and acceleration of an object on the surface of the Earth, assuming a spherical Earth. The original poster presents a problem involving the Earth's rotation and seeks assistance with their calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate linear speed and acceleration using formulas related to angular motion but questions the validity of their results. Participants inquire about the source of a specific figure used in the calculations, indicating a focus on understanding the parameters involved.

Discussion Status

The discussion is ongoing, with participants clarifying the period of the Earth's rotation and addressing potential errors in the original poster's calculations. There is a collaborative effort to ensure the accuracy of the values used in the formulas.

Contextual Notes

Participants are examining the implications of the sidereal day duration and its impact on the calculations, highlighting the importance of accurate figures in solving the problem.

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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