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.