Gravity Effectively Isn't Constant

Consider a spherical planet with radius \(R\), that is rotating with angular velocity \( \omega \) about it's axis. The lattitude \(x\) of a point \(P \) that is a height of \(h\) away from the equator, is denoted as \( x = \frac{h}{R} \). Suppose that the acceleration due to gravity at the North pole is \(g\), then what is the effective acceleration ar point \(P\) in terms of the latitude \(x\)?

  • \(T \cos x\) is the Centrifugal force along the tangent for rotation.
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