Centripetal force equaling 1G?

Question

Can any one provide me a equation showing a relationship of radius/diameter and Rotation speed taht always equals 1 G at the circumference. Much appreciated ;)

Answer 1

Here we are equating acceleration.

For a body in circular motion, acceleration is given by v^2/r.

Then

g=v^2/r

v=sqrt(r*g).

This is the same equation given by the fellow above me, but he makes a mistake. He says that omega=sqrt(r*g). This is wrong.

w, or omega, is the rotational speed which you seek. However, v is the tangential speed at the radius, not the angular speed, w.

w=v/r

v=sqrt(r*g)

So

w=sqrt(r*g)/r

w=sqrt(r*g)/sqrt(r^2)

w=sqrt(g/r)

THIS is the true angular speed.

Answer 2

David Z is correct. Please note that the angular speed ω (omega) is expressed in "radians per second." If you want to know the answer in revolutions per second, divide ω by 2π:

revs. per second = ω/(2π) = sqrt(g/r) / (2π)

If you want to know the "period" (number of seconds it takes to go around once), flip that upside down:

period = 2π / sqrt(g/r)

Answer 3

omega=sqrt(r*g) where omega-angular velocity, r-radius, g-gravitational acceleration