Earth's Rotation & g-Force Effects

[phymatter]

if the Earth stops rotating , what will happen to the apparent value of g on its surface ?

 

[Drakkith]

The force of gravity would be unaffected I believe. Without the rotation you might be able to measure a slightly higher amount of G on stationary objects on the ground since the surface isn't rotating anymore, but the amount would probably be negligible.

 

[Rap]

The force of gravity would be unaffected I believe. Without the rotation you might be able to measure a slightly higher amount of G on stationary objects on the ground since the surface isn't rotating anymore, but the amount would probably be negligible.

If you dropped something, it would have a slightly higher acceleration downward, because there would be no centripetal acceleration.

 

[AlephZero]

The force of gravity would be unaffected I believe. Without the rotation you might be able to measure a slightly higher amount of G on stationary objects on the ground since the surface isn't rotating anymore, but the amount would probably be negligible.

The effect is small but big enough measure with simple experiments. The early global explorers found that their pendulum clocks ran slower as they traveled towards the equator. The change in length of a pendulum with a period 1 second is a few mm, between the poles and the equator.

There was considerable debate as to the cause of this (one hypothesis was that gravity was temperature-dependent) before Newton sorted out the math.

 

[Drakkith]

Just like i thought then.

 

[D H]

if the Earth stops rotating , what will happen to the apparent value of g on its surface ?

The Earth's rotation affects g in two ways. Directly, g includes a centrifugal acceleration term. This will vanish should the Earth stop rotating, thereby increasing the apparent value of g except at the poles. Indirectly, the Earth's rotation makes the Earth have a shape of an oblate spheroid. The Earth would presumably relax to a spherical shape should the Earth stop rotating. This would bring equatorial regions closer to the center of the Earth but make polar regions move further from the center of the Earth.

Assuming the Earth's volume remains constant while it relaxes toward this spherical shape, the radius of the Earth would become a uniform 6371.0008 km sometime after the Earth stopped rotating. The product G*M_earth=398,600.4418 km³/s² would remain unchanged (mass isn't lost), so g would become 9.82024802 m/s² for all points on the new surface of the Earth at sea level.

A couple of formulae for computing the apparent value of g at sea level (with the Earth still rotating) are the 1967 Geodetic Reference System Formula

$$g_0 = 9.780327\,\left(1+0.0053024\sin^2\phi-0.0000058\sin^2(2\phi)\right)\,\frac{\mbox{m}}{\mbox{s}^2}$$

and the World Geodetic System 1984 equation

$$g_0 = 9.7803267714\,\frac{1+0.00193185138639\sin^2\phi}{\sqrt{1-0.00669437999013\sin^2\phi}}\,\frac{\mbox{m}}{\mbox{s}^2}$$

To seven places, both formulae yield an acceleration of 9.820248 at a latitude of 61.381°.Bottom line: Should the Earth stop rotating the apparent gravitational acceleration would increase for latitudes less than 61.381° but decrease for more extreme latitudes.