Fastest Planet Rotation: Calculating Period using Volume & G

[john_simpson]

The fastest rate of rotation of a planet is that for which the gravitational force on matter at the equator just provides the centripetal force necessary for that matter to move with circular motion. Show that the period of rotation in this case is given by T= √3π/Gp where the planet is assumed to be a uniform sphere of density p (which has units of kgm^3(



Volume sphere = 4/3πr^3
Universal Gravitational Constant = 6.67 x10^-11



I truly have no idea where to start please help!

 

[Doc Al]

Imagine a small mass on the surface of the planet at the equator. What is its acceleration? What is the force on it? Apply Newton's 2nd law.

Hint: Review centripetal acceleration' and Newton's law of gravity.