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

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SUMMARY

The discussion focuses on calculating the angular speed required for a person at the equator to experience a weight reduction of 25%. The relevant equations include the centrifugal force equation, F = m r ω², where ω represents angular speed in radians per second, and the weight equation, wt = mg. The user attempts to derive the necessary angular speed by equating wt to 0.75 times the gravitational force, mg, but seeks further guidance on integrating weight and angular speed in their calculations.

PREREQUISITES
  • Understanding of angular speed and its units (radians per second)
  • Familiarity with gravitational force calculations (wt = mg)
  • Knowledge of centrifugal force and its relation to mass and radius
  • Basic algebra for manipulating equations
NEXT STEPS
  • Research the derivation of centrifugal force in relation to angular speed
  • Learn how to apply the concept of centripetal acceleration in rotational motion
  • Study the effects of varying angular speeds on weight at the equator
  • Explore real-world applications of angular speed in physics and engineering
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Students in physics, educators teaching rotational dynamics, and anyone interested in the effects of Earth's rotation on weight perception.

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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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