(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine the speed with which the earth would have to turn to rotate on its axis so that a person on the equator would weigh 3/4 as much

2. Relevant equations

V_{T}=r*ω ; V_{i}=469 m/s is tangential velocity of earth

ƩF=M*a_{c}=m*V_{t}^2/r

3. The attempt at a solution

The positive direction is toward the center of the earth.

From ƩF=m*a_{c}

Initial: m*g-N_{i}=m*V_{i}^2/r

Final: 3/4m*g-N_{f}=m*V_{f}^2/r

Since m*g is the same for initial and final state I assume that N_{i}=N_{f}

Therefore:3/4m*g-[mg-m*V_{i}^2/r]=m*V_{f}^2/r or

V_{f}=Sqrt(V_{i}^2-r*g/4)

I have a sign error. I end up taking the square root of a negative number but the physics looks OK. Suggestions?

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# Homework Help: Tangential velocity of the earth

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