Frictionless world - Earth rotation

[autodidude]

Main Question or Discussion Point

If the world was frictionless, would the Earth orbit underneath your feet? Would buildings and things attached to the ground be slamming into you at the same speed as the Earth's rotation?

 

[CWatters]

What happens when you step out onto the ice at an ice rink? Why?

 

[autodidude]

You slide because of low friction...I asked this cause I wasn't sure if there's anything else involved

 

[voko]

If the world was frictionless, you would not be able to fix anything onto anything else, not even with slamming, because that also depends on friction.

 

[russ_watters]

It really isn't answerable: what happens to an object on a frictionless surface depends on how it got there.

 

[jtbell]

What happens when you step out onto the ice at an ice rink? Why?

You slide because of low friction...

But not at anywhere near the earth's rotational speed, right? And if you step onto the ice the right way, very very carefully, you don't slide.

 

[autodidude]

If the world was frictionless, you would not be able to fix anything onto anything else, not even with slamming, because that also depends on friction.

How's friction involved when you slam into something?

It really isn't answerable: what happens to an object on a frictionless surface depends on how it got there.

But not at anywhere near the earth's rotational speed, right? And if you step onto the ice the right way, very very carefully, you don't slide.

Oh yeah, I forgot about the whole inertial frame part (which got me thinking, since the Earth is rotating, does gravity have anything to do with centripetal force?)

Say you landed on Earth from space, there would be a difference in velocity, right? But then, doesn't that already happen in our world with friction?

 

[CWatters]

does gravity have anything to do with centripetal force?

Not sure what you mean but... If you put a known mass on accurate weighing scales they read differently at the poles vs the equator due to centrifugal force. In effect some of the gravitational force is used up providing the necessary centripetal force.

 

[voko]

How's friction involved when you slam into something?

Twice. First, you have to be attached to the surface of the Earth - rotating - before you can start slamming. Second, after you have managed to slam something into the Earth the only force holing the object slammed into the Earth would be friction. Absent that, the object will be pushed back to the surface by the centrifugal force.

 

[autodidude]

@CWatters: I just remembered some stuff with circular motion where there's a force directed towards the centre when i

 

[jartsa]

If the world was frictionless, would the Earth orbit underneath your feet? Would buildings and things attached to the ground be slamming into you at the same speed as the Earth's rotation?

Let's say buildings are built into potholes on a frictionless surface. When you step out of one such building, you will start to slide with accelerating speed towards the equator, but only if the Earth is a perfect sphere.

If the road you are stepping onto is perfectly horizontal according to a spirit level, then you don't slide anywhere.

 

[mikeph]

I think there is a very subtle thing going on here

If you start this thought experiment with the person rotating with the Earth, then the non-axial component of their weight will contribute to their rotation and keep them at the same longitude. However this leaves an axial component of their weight which cannot be fully cancelled by the reaction force of the Earth which acts upwards. The resultant force acts tangentially North/South towards the equator, and the person's latitude will exhibit simple harmonic motion about the equator.

If the person is started from rest with no friction however, then no part of their weight is used in circular motion and the weight can be exactly opposed by the reaction of the surface. They will stay still.

Anyone agree?/disagree?

 

[ImaLooser]

If the world was frictionless, would the Earth orbit underneath your feet? Would buildings and things attached to the ground be slamming into you at the same speed as the Earth's rotation?

It would depend. If you started out on a flat surface with the same rotational speed as the earth then you would rotate in place wherever you were. I guess the wind would blow you around. In the northern hemisphere the Coriolis force would curve your path to the right.

If you were on a non-flat surface then you'd slide to the bottom of whatever then up the other side, then back down, over and over and over. It probably wouldn't repeat the same path. I guess air resistance would eventually damp it out.

If you started on a flat surface at rest with respect to the stars then you would suddenly be in wind of up to 1000km/hour. The blast would kill you unless you were close to the poles, which would present other problems of survival.

 

[autodidude]

@CWatters: I just remembered some stuff with circular motion where there's a force directed towards the centre when i

Sorry, this was typed on a phone. I abandoned ship halfway and didn't think it posted.

What I meant to say was I remembered that with circular motion, there's a force directed to the centre and wondered if that had anything to do with gravity

Twice. First, you have to be attached to the surface of the Earth - rotating - before you can start slamming. Second, after you have managed to slam something into the Earth the only force holing the object slammed into the Earth would be friction. Absent that, the object will be pushed back to the surface by the centrifugal force.

@voko: What if the object was attached to the Earth? Would you just be pushed back?

@jartsa: Why would you be accelerated towards the equator?

There seems to be a lot more going on than I thought!

 

[voko]

@voko: What if the object was attached to the Earth? Would you just be pushed back?

You see, there is a contradiction. When something can be attached to something else, that means we have some forces at the atomic level; and those same forces are responsible for friction. So it is quite unphysical to think of a frictionless world where some attachments are possible. But if assume this, we have to consider all the other factors. For example, the atmosphere. Is it present? Is it revolving with world? Does it have friction with bodes immersed into it?

 

[autodidude]

How about a mountainside? That would be considered to be part of the Earth, right?

With the atmosphere, how does it revolve with the world?

 

[mikeph]

That is another assumption- that the Earth is a rigid body held together by something other than friction.

 

[jartsa]

Let's say Bob is standing on the north pole of a frictionless spinning ball. Centrifugal force is pulling Bob's left side to the left, and right side to the right. When Bob extends his left arm he starts sliding to the left, pulled by the centrifugal force.

If the ball is the same size as the earth and spins at the same rate as the earth, Bob's speed will be about 600 m/s towards the south pole at the equator. And also the surface of the ball is rotating under Bob at the speed that the surface has.

Oh yes, when standing on the north pole, Bob should spin with the ball, there's no centrifugal force otherwise.

 

[voko]

Oh yes, when standing on the north pole, Bob should spin with the ball, there's no centrifugal force otherwise.

If there is no friction, why would he?

 

[jartsa]

If there is no friction, why would he?

I don't know, but he can spin at any rate except at zero rate, and still be effected by centrifugal force.

This makes me feel that the story went quite seriuosly wrong though.

 

[voko]

I don't know, but he can spin at any rate except at zero rate, and still be effected by centrifugal force.

This makes me feel that the story went quite seriuosly wrong though.

That's the whole issue here. There is no friction, he is not strapped to the Earth. He can only move inertially and be affected by gravity, but not the rotation of the Earth. Well, at least till we figure out what the atmosphere does to him.