Rate of rotation?

The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator barely provides the centripetal force needed for the rotation. For a planet with a uniform density of 8.8 g/cm3, typical of many planets and asteroids, evaluate the shortest period of rotation.

Rate of rotation?

Centripetal acceleration = (V^2)/R

http://en.wikipedia.org/wiki/Centripetal...

Acceleration due to gravity = GM/(R^2)

http://en.wikipedia.org/wiki/Gravity

At the shortest period of rotation, they are equal so

(V^2)/R = GM/(R^2)

G is the universal gravitational constant.

M is the volume of the sphere of radius R times the density

The period of rotation = distance/velocity = 2(pi)R/V