Does Standing at the Earth's Poles Affect Your Balance?

[skeletonic]

Ok so some main postulates: The Earth is spinning. That would be like a wheel, but a lot bigger. It would have to have angular momentum.. right? (rhetorical) So we do indeed have an axis on which Earth spins... but we all know it is imaginary. So now for my real questions.. hope your not disappointed.

If there was to be an exact point- two of them for a sphere- in which the Earth spun about as an axis, and it was pinpointed... would standing there give you more balance than any other spot on earth, besides the other axis?

So qusetion two is along the same lines as question one.

Starting from the north pole, you start measuring straight down to the south pole. Say you got 2000 million km as the distance... just a random number. with this number you could find an average center.. or equator.

So if gravity is the same everywhere on the surface of earth.. is the outward force from angular momentum also the same everywhere?
Would you be able to jump higher if you were located on the equator?
If the Earth stopped spinning, would we all be crushed by gravity?
Is the Coriolis Effect more evident arround the equator?

This last question is sort of dum, if you were starting to fall backwards, and then *pop* you were standing 90 degrees to where you were, would you still be falling backwards?

Ok sorry about any mistakes i may have made, but that is all for now..

 

[vanesch]

If there was to be an exact point- two of them for a sphere- in which the Earth spun about as an axis, and it was pinpointed... would standing there give you more balance than any other spot on earth, besides the other axis?

There is always an instantaneous axis of rotation to a rigid body (that's a kinematic fact about the motion of rigid bodies - as far as we can take the Earth as being a rigid body). Every conceivable, continuous motion of a rigid body can be decomposed instantaneously in a translation motion of the center of gravity and a rotation about an axis through that center of gravity. This is just a theorem in the kinematics of rigid bodies. Of course, the axis of rotation is time-dependent, and so is the translation, for an arbitrary motion. For a body rotating freely (like the Earth is, if we exclude small torques due to uneven distribution of matter), there are equations spelling out how this instantaneous axis of rotation should evolve over time: they are called the Euler equations of rigid body motion. The translational motion and the rotational motion are highly decoupled. In fact, the translational motion follows very closely the motion a matter point placed at the center of gravity, with mass = mass of the earth, would undergo under influence of the gravitational attraction of the other bodies (mainly sun and moon).

As such, we can, to a very good approximation, study the rotational motion of the Earth independently of the translational motion.
The Euler equations show also that the axis of rotation will remain about constant if it is an axis of symmetry (a major axis of revolution ; an eigenvector of the tensor of moments of inertia of the rigid body).

And as such, we arrive, at a good approximation, that we can study the Earth rotation as a rotation around a more or less fixed axis of rotation.

Starting from the north pole, you start measuring straight down to the south pole. Say you got 2000 million km as the distance... just a random number. with this number you could find an average center.. or equator.

So if gravity is the same everywhere on the surface of earth.. is the outward force from angular momentum also the same everywhere?

No, of course not, because it is dependent on the distance to the axis of rotation (the centrifugal force). At the pole, that distance is essentially 0, so you only have the pure gravity force. At the equator, it will be maximal, and pointing upward. In between, it will be pointing sideways.

Would you be able to jump higher if you were located on the equator?

Yes. A very small bit. Because the centrifugal force (calculate it !) is very tiny as compared to the gravity force.

If the Earth stopped spinning, would we all be crushed by gravity?

No, the correction is very tiny.

Is the Coriolis Effect more evident arround the equator?

Yes.

This last question is sort of dum, if you were starting to fall backwards, and then *pop* you were standing 90 degrees to where you were, would you still be falling backwards?

At relatively low speeds, the coriolis force is also rather tiny. If you're falling backwards due to gravity, you'll essentially be falling backwards, with or without these tiny corrections.

cheers,
Patrick.

 

[kyle8921]

I would like to address the content and questions presented in this post. Firstly, I appreciate your curiosity and interest in understanding the Earth and its movements. I will try my best to answer your questions and clarify some concepts.

Firstly, you are correct in saying that the Earth is spinning and this is known as its rotation. This rotation does give the Earth angular momentum, which is a measure of how much an object is rotating. However, the Earth's rotation is not like a wheel spinning on an axle. It is more like a spinning top, where the axis of rotation is not fixed but instead wobbles slightly due to the gravitational pull of the Moon and Sun.

Regarding your first question, if there was an exact point where the Earth's axis of rotation passed through, this point would not give you more balance than any other spot on Earth. This is because the Earth's rotation and gravity affect all points on its surface equally. The only difference would be the direction of the gravitational force, which would be perpendicular to the surface at the poles and parallel to the surface at the equator.

Your second question is also related to the Earth's rotation and its effect on the distance from the North Pole to the South Pole. However, the distance between the poles is not a random number and is actually around 40,000 km. This distance does not determine the Earth's equator, but rather the equator is defined as the imaginary line that divides the Earth into the Northern and Southern Hemispheres.

To answer your third question, the outward force from angular momentum is not the same everywhere on Earth. This is because the Earth's rotation is not constant at all points on its surface. The closer you are to the poles, the slower the rotation, and the closer you are to the equator, the faster the rotation. This means that the outward force from angular momentum is strongest at the equator and weakest at the poles.

As for your last question, if the Earth suddenly stopped spinning, we would not all be crushed by gravity. This is because the Earth's gravity is not dependent on its rotation, but rather on its mass. However, the sudden stop of rotation would have other consequences, such as changes in weather patterns and the length of the day.

Lastly, the Coriolis Effect is not more evident around the equator. It is actually strongest at the poles and weakest at the equator. This is because the Coriolis Effect is