Frictionless world - Earth rotation

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

 

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.

 

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.

 

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.

 

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.

 

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?

 

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.

 

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?

 

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

 

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.

 

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.

 

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.