Factor to increase Earth's rotation speed for equatorial centripetal acceleration of g

[JasonRox]

The book is asking me to find...

c) by what factor would the speed of the Earth's rotation have to increase for a body on the equator to require a centripetal acceleration of g to keep it on the earth?

 

[TheDude710]

Find where centripetal acceleration = g. so a=w^2 * r. where w is angular velosity and r is radius of earth. make g=w^2*r, solve for w. then see that the ratio of w is to the actual angular velosity of earth. What is actually happening at this point is the Earth ( and therefore you) is spinning just fast enough to make you feel weightless. You will be orbiting the Earth right on its surface, pretty cool,huh?

 

[JasonRox]

Thanks.

That's what I thought. It is worth marks, so I had to make sure I had it.