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The Magnitude and Direction of Centripetal Acceleration

What is the magnitude and direction of the centripetal acceleration due to the earth's rotation at a location near Kansas City at 38 degrees latitude? I believe the answer is 2.66x10^-2 m/s^2, towards the earth's rotation axis. I need to see all formulas involved.

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This solution provides a step by step solution with diagrams to find the magnitude and direction of centripetal acceleration.