Tangential velocity of the earth

[RTW69]

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?

 

[haruspex]

Nf is to be 3/4 of what? And what equation tells you what it will actually be? (Your 'Final' equation is completely wrong.)

 

[RTW69]

OK, Final:m*g-3/4*N=m*V_f^2/r

 

[haruspex]

Looks right, if N is what you wrote as Ni previously,