What Angular Speed Must Earth Rotate for Equatorial Weight to Drop by 25%?

AI Thread Summary
To determine the angular speed required for a person at the equator to weigh 75% of their current weight, the centrifugal force must counteract part of the gravitational force. The equations involved include the relationship between angular speed (w), radius (r), and gravitational acceleration (g). The user attempts to calculate the new weight using the equation wt = 0.75 x m x 9.8 but struggles to connect weight and angular speed. The key equation to use is the centrifugal force equation, F = m r w^2, which relates angular speed to the desired reduction in weight. Further assistance is sought to clarify the connection between these variables.
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Angular Speed of Earth when...

Homework Statement


Determine the angular speed with which the Earth would have to rotate on its axis so that a person on the equator would weigh 75% of their present weight (Radius of the Earth is 6400 km)


Homework Equations



wf=2pi/T
wt= mg
v=wr


The Attempt at a Solution


First I did wt=0.75 x m x 9.8, the problem is i can't find any equation that could incorporate weight and angular speed. Can somebody please give me some hints? Any help would be appreciated:) Thankyou very much
 
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Centrifugal force = m r w^2 where w is the angular speed in radians/sec.
 

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