Gravity, friction and tangential velocity

[razidan]

Hi everyone,
Me and a friend discussed a problem relating to a rotating reference frame, and somehow got to this question which we can't fully figure out, or maybe we are missing something. so, here goes:

On Earth's equator, our tangential velocity is ~1700 km/hr. A satellite orbiting right above the surface would have a tangential velocity of ~27000 km/hr.
So, if we were free falling (at height "0"), we were supposed to be a lot faster then we are. so what is making us move that much slower (and at the poles, even at zero speed)? is it friction?
if it is friction, is friction changing the magnitude of our velocity while gravity is changing the direction (so that we remain on the ground, and not fly off tangentially).

thanks,
R.

 

[mfb]

Why do you expect to be in a circular orbit if you are jumping around at the equator?

If you jump up from the ground, you have the velocity of the ground plus a bit of upwards motion from your muscles. A change in velocity (e.g. to reach orbit) would need a force acting on you. Gravity just pulls you downwards, and doesn’t do that very fast.

 

[Delta2]

When you do "free falling " (e.g when you go up with an airplane and then fall with a parachute) it isn't exactly free falling, you still have the component of tangential velocity of 1700km/hr and the ground has the same tangential velocity , so you move relative to the ground with zero tangential velocity (or almost zero, in any case much smaller than the 1700km/h), that's why you can't see how fast you are moving..

Friction or air resistance has nothing to do with the above fact.

 

[A.T.]

we were supposed to be a lot faster then we are

Supposed by whom?

 

[razidan]

Thanks for the response. I guess the question is unclear, so I'll ask it in a different way.
If the Earth was completely frictionless (and a perfect smooth sphere), what would happen to me?
Would I see everything rushing past me at 1700 km/hr?

 

[stevendaryl]

Thanks for the response. I guess the question is unclear, so I'll ask it in a different way.
If the Earth was completely frictionless (and a perfect smooth sphere), what would happen to me?
Would I see everything rushing past me at 1700 km/hr?

I don't see what friction has to do with anything, except for the fact that objects on the surface of the Earth tend to be stationary with respect to that surface, because of friction. But even without friction, an object that is initially at rest relative to the ground would remain at rest---as long as the surface of the Earth is stiff enough to hold it up.

An object on the surface of the Earth is not in freefall, because the Earth is pushing up on it. That's not friction, that's what's called the "normal force", because its direction is normal (perpendicular) to the surface.

 

[Delta2]

Thanks for the response. I guess the question is unclear, so I'll ask it in a different way.
If the Earth was completely frictionless (and a perfect smooth sphere), what would happen to me?
Would I see everything rushing past me at 1700 km/hr?

Yes, if you were "left" on Earth having 0 absolute tangential velocity.
No, if you were left on Earth having 1700km/hr absolute tangential velocity on the same direction of rotation.

I mean if you go now and stay above a totally frictionless surface you will see everything around you as stationary because you "already" have tangential velocity of 1700km/hr, same as that of the ground, so relative velocity to the ground is zero.

EDIT: Ok I think I see your point now, what keeps us in circular orbit around Earth at only 1700km/h while a satellite just above the surface of Earth would have 27000km/hr? Its friction, other contact forces, and gravity.

 

[A.T.]

If the Earth was completely frictionless (and a perfect smooth sphere), what would happen to me?

You would land on your butt a lot?

Would I see everything rushing past me at 1700 km/hr?

If you would somehow get so fast relative to "everything".

 

[Delta2]

It's the normal force actually that keeps us in circular orbit though our tangential speed is "low" only 1700km/h. The net force Gravity Force -Normal Force plays the role of centripetal force.

 

[mfb]

If the Earth was completely frictionless (and a perfect smooth sphere), what would happen to me?

That depends on your initial velocity. If you are standing around and suddenly lose friction nothing special will happen. You are now unable to move away from your current location, however, unless you happen to have a rocket with you (or something equivalent). If you lose friction while you walk around, you'll keep sliding around forever. Your track (relative to the ground) will be a large circle thanks to the Coriolis force.

 

[Orodruin]

You are now unable to move away from your current location, however, unless you happen to have a rocket with you (or something equivalent). If you lose friction while you walk around, you'll keep sliding around forever. Your track (relative to the ground) will be a large circle thanks to the Coriolis force.

I am not sure that this is accurate. Take away the friction and it should not matter that the Earth is spinning underneath. In the non-rotating frame, the path will then be a great circle. You can then get the motion relative to the Earth by transforming to the rotating Earth frame. The result would be oscillations about the equator with a westward component everywhere but at the turning points if you start from rest (in order for angular momentum to be conserved). If you start out on the equator or at a pole, you clearly will remain in place unless given an initial velocity.

Edit: The above assumes that the Earth is a perfect sphere (which it isn't). If it is not, things will work out differently. In particular, the initial acceleration in the equatorial direction in the case of the sphere is due to the projection of the centrifugal force due to the rotation onto the surface. If the Earth is not a sphere this component may be canceled or partially canceled by a component of gravity that is not orthogonal to the surface.

 

[mfb]

If we assume a perfect sphere then you will oscillate around the equator, but if we assume an oblate spheroid as an equipotential surface (=the current oceans, to a good approximation*) you do not (necessarily).

*for deviations, please consult your old avatar

Thinking further about this: It doesn’t have to be a circle. If you start at a pole with a slow speed your track on a globe will be a spiral.
Anyway, this side-discussion is probably not helping.