How fast would the world have to spin for someone standing on the equator to weight half what they weigh?

well if a due to gravity is 9.81m/s^2 you would want centripetal accelerating to be half that, or about 5.9m/s^2.

Centripetal accel is =R*w^2

R is the radius of the earth, 6366.2m at the equator.

Rotational velocity would be Sqrt(5.9/6366200) = 9.627x10^-4

compare that to the rotational velocity we have now ,

1 rev/24hrs= 6.28rad/day = 7.27x10^-5 rad/sec, and the world would have to spin about 10 times faster for a person to feel half as heavy.

I assume you mean how fast does the world have to spin for centripetal force to equal gravitational force, giving you the illusion of weightlessness. People on the space shuttle are subject to the same gravity that we are they just have the illusion of weightlessness because they are falling with gravity and the curvature of the earth. So to answer your question, the space shuttle travels 17000mph, earth is about 26000 miles around, so the earth would need to spin once every 1.5 hours to achieve this.

Weight is a function of mass and gravitational pull. Increasing the rotational speed of the earth would not affect either of these.

slower