QUESTION #277

# How fast would the Earth have to rotate so that it would neutralize gravity?

In order to neutralise the acceleration due to gravity the centripetal acceleration needs to be equal to the acceleration due to gravity:

Centripetal acceleration = 9.81 m/s2

The centripetal acceleration is, a:

a=r x w2

Where r is the Earth's radius (in our case the radius at the equator), and w is the angular velocity.

Let a = 9.81 m/s2 and r = 6.4 x 106 m

9.81 = 6.4 x 106 x w2

Therefore w = 0.00124 rad/s

This is how fast the Earth would need to rotate to get centripetal acceleration at the equator equal to 9.81 m/s2.

So if we use this value in this equation:

w = 2/T

Where w is the same as before, the numerator is constant, and T is the time for rotation or the period.

If we put our value of omega (angular velocity) into the equation we find that T = 5074.99 seconds or 1.409 hours. This means that the Earth would need to rotate with a period of 1 hour 24 minutes. This means it would need to rotate approx. 20 times faster than it does now!
Answered by: Dan Summons, Physics Undergrad Student, UOS, Souhampton