- #1

RTW69

- 374

- 1

## Homework Statement

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

## Homework Equations

V

_{T}=r*ω ; V

_{i}=469 m/s is tangential velocity of earth

ƩF=M*a

_{c}=m*V

_{t}^2/r

## 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?