Can some help me explain what they are trying to say

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In summary, the conversation discusses finding the necessary increase in Earth's rotation speed for a body on the equator to experience a centripetal acceleration of g. This is achieved by setting the equation a=w^2 * r, where a is the centripetal acceleration, w is the angular velocity and r is the radius of Earth, equal to g and solving for w. The resulting ratio of w to the actual angular velocity of Earth explains the feeling of weightlessness experienced at this point, as the Earth is spinning just fast enough for the body to orbit along its surface.
  • #1
JasonRox
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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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  • #3
Thanks.

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

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