Can some help me explain what they are trying to say

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The discussion focuses on calculating the required increase in the Earth's rotational speed for a body at the equator to experience a centripetal acceleration equal to gravitational acceleration (g). The formula used is g = w^2 * r, where w represents angular velocity and r is the Earth's radius. By solving for w, participants determine the ratio of this theoretical angular velocity to the Earth's actual angular velocity. The conclusion highlights that at this increased speed, a person would feel weightless, effectively orbiting the Earth at its surface. This calculation is deemed important for academic purposes.
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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?
 
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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?
 
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Thanks.

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

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