(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

It's a high school physics question that I remembered and need to understand for curiosity's sake. I'm stating the problem in my own words, so it is likely that I may be asking a wrong question. Here it is nonetheless:

Derive an expression that shows that the major variable affecting the rotation period of a planet is its density [assuming planet is a perfect sphere & mass is evenly distributed].

2. Relevant equations

Newton's law of gravitation: F = G*M*m/r^2

Centripetal force: F = m*v^2/r and v = 2*Pi*r/T

Density: rho = m/v

3. The attempt at a solution

Assuming the rotation is due to a centripetal force (which is due to the gravitational attraction of the surface mass and the rest of the planet's centre of mass) acting on the surface of the planet, I get this as my final expression for the period, T:

T = [tex]\sqrt{(3*Pi)/(G*rho)}[/tex]

(I'm unable to get (3*Pi) and (G*rho) in brackets like this, for Latex)

The problem is that when I substitute the value of the density of Earth (5515 kg/m^3), I don't get anywhere near the actual 24 hours that I should.

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# Homework Help: Period of Earth's Rotation

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