[Bored chemist]

Just  for a moment, let's imagine I can start + stop the Earth spinning without the inconvenience of everything getting thrown about.
I stop the spin and hang up a plumb line.
I draw a spot on the floor where the line points.
Then I restart the earth.
Yes, the plumb line no longer points where it did. It is very slightly out of line (Good luck measuring the change).
The plumb line now points at a slightly different spot on the floor. (It now points at a spot slightly nearer the equator)

But once the Earth is up to speed, there's nothing acting on the plumb line to make that point change.
Now, from the point of view of a distant observer, the line does trace out a curve. It is very nearly a cone with the centre of the Earth near  the apex.

But there's no reason for it to change.

[Janus]

I do not expect a hanging item to swing.

But if there is an inertial force due to the movement of earth on every item on earth, then I do expect a hanging item to be displaced under that force.

A simple experiment will show that if you have an item hanging from a hanging base and you move the base, the item will be displaced from its vertical position.

I expect the same to happen with any hanging item due to earth's movement, ie the rope should not be exactly perpendicular but rather at an angle from the perpendicular axis.

Perpendicular to what?  If I have a spirit level, it is subject to the same combined forces and thus will indicate that "level" is exactly perpendicular it the hanging object's line.
If you consider an "ideal" surface for the Earth (no irregularities), Then this surface is a that of an oblate spheroid, the shape of which is defined by those same combination of effects ( The Earth is not rigid, but rather consists of a relatively thin crust floating on a liquid mantle layer. Again, the object will hang perpendicular to that surface at every point.
If the Earth were a rigid sphere which did not deform under the these influences, then, yes you could measure a non-perpendicular angle between hanging object and the surface, but this is not the case.

[evan_au]

Oops! overlap with Bored Chemist & Janus, with essentially the same point...

the rope should not be exactly perpendicular but rather at an angle from the perpendicular axis.

ok, so where do you get your "perpendicular axis" from which to measure the angle?

The traditional method used by builders was to attach a metal weight to a piece of string: a "plumb bob". Only this will be displaced from the vertical, too! So you won't measure any difference.

Maybe you could use the average sea level (ignoring tides, of course). But if there was any sideways force on the ocean, the water would all flow in that direction, And in fact, a lot of ocean has flowed towards the equator, building up a mound of water that is several kilometers high (compared to the poles). So you won't measure any difference there, either.

Your best evidence in a small space is the Foucault pendulum (ie without going out to measure the world, as was attempted when defining the meter in the metric system).

[Kryptid]

(cough) zero point energy (cough)

Then I'll make a correction: swing enough for a casual observer to notice the rotation of the Earth.

[scientizscht (OP)]

Just  for a moment, let's imagine I can start + stop the Earth spinning without the inconvenience of everything getting thrown about.
I stop the spin and hang up a plumb line.
I draw a spot on the floor where the line points.
Then I restart the earth.
Yes, the plumb line no longer points where it did. It is very slightly out of line (Good luck measuring the change).
The plumb line now points at a slightly different spot on the floor. (It now points at a spot slightly nearer the equator)

But once the Earth is up to speed, there's nothing acting on the plumb line to make that point change.
Now, from the point of view of a distant observer, the line does trace out a curve. It is very nearly a cone with the centre of the Earth near  the apex.

But there's no reason for it to change.

You say 'there's nothing acting on the plumb line to make that point change' and then you say 'the line does trace out a curve'. Not clear how can these occur at the same time.

My point is that if the plumb bob's tip can write on the ground, then it will draw a circle or ellipse in 24h. Don't you agree?

Also, how can you say 'there is nothing acting on the plump bob' when we clearly see the force below changing direction:

https://en.wikipedia.org/wiki/Foucault_pendulum#/media/File:Foucault_pendulum_plane_of_swing_semi3D.gif

[alancalverd]

It is precisely because there is no rotational force acting on the pendulum, that the earth rotates below it.

If you want to look at the earth producing rotational forces on real objects, have a look at the Coriolis component of wind.

[Janus]

Just  for a moment, let's imagine I can start + stop the Earth spinning without the inconvenience of everything getting thrown about.
I stop the spin and hang up a plumb line.
I draw a spot on the floor where the line points.
Then I restart the earth.
Yes, the plumb line no longer points where it did. It is very slightly out of line (Good luck measuring the change).
The plumb line now points at a slightly different spot on the floor. (It now points at a spot slightly nearer the equator)

But once the Earth is up to speed, there's nothing acting on the plumb line to make that point change.
Now, from the point of view of a distant observer, the line does trace out a curve. It is very nearly a cone with the centre of the Earth near  the apex.

But there's no reason for it to change.

You say 'there's nothing acting on the plumb line to make that point change' and then you say 'the line does trace out a curve'. Not clear how can these occur at the same time.

My point is that if the plumb bob's tip can write on the ground, then it will draw a circle or ellipse in 24h. Don't you agree?

The plumb bob will continually point at the same point of the Earth's rotational axis, and since the line drawn between that point and the hanging point of the plumb bob always passes through the same point on the surface. So no, the plumb bob tip does not trace out a circle on the ground. 

[Bored chemist]

My point is that if the plumb bob's tip can write on the ground, then it will draw a circle or ellipse in 24h. Don't you agree?

No.
That's why I had already said

But once the Earth is up to speed, there's nothing acting on the plumb line to make that point change.

What variable force do you think is pushing it?
The centrifugal force is constant (In the coordinate frame of the surface of the Earth), gravity is constant .
What changes to make the point move?

[syhprum]

The pendulum will only swing if the rate of rotation changes as the Earths rotation rate is low and daily changes only amount to microseconds you are not going to see much swinging.

[scientizscht (OP)]

Okay, so the plumb bob's line won't be pointing to the point it would point if earth was not rotating. The earth's rotation makes the plumb bob point to a different point due to inertial force. You are also saying that this inertial force is constant in its magnitude and direction which I am not sure but I can buy it.

What is the magnitude of that inertial acceleration?

[Halc]

What is the magnitude of that inertial acceleration?

Centripetal acceleration at earth surface is about 3.4sinΦ cm/secē towards the axis (not downward) where Φ is your latitude.  That's about 0.0035 g's at the equator.

Make a foam plank and affix an arrow at the middle of it pointing straight down (perpendicular to the plank).  Float that on calm water.  The arrow will point the same way as the plumb line anywhere on Earth, but not exactly at the center of Earth in most places.

[scientizscht (OP)]

Okay, so you are saying that the inertial force acting on every object on earth due to the earth's rotation has constant direction related to earth that results in the plumb bob to point to a displaced point in comparison to the point if earth was immobilised instead of tracing a circle.

If this is true, then why Foucault's pendulum plane of swing rotates? If the force was constant in direction, then the plane of swing would not rotate, it would simply be displaced altogether in comparison to what the plane would be if earth was immobilised (due to the inertial force's component that is perpendicular to the plane of swing) and also there would be  reduction in the swing breadth (from the component of the inertial force that is parallel to the plane of swing).

[Halc]

If this is true, then why Foucault's pendulum plane of swing rotates?

It doesn't.  Earth rotates around it.

[scientizscht (OP)]

If this is true, then why Foucault's pendulum plane of swing rotates?

It doesn't.  Earth rotates around it.

Then the rotation of Foucault's pendulum is due to the rotation of the observer who stands on the rotating earth. That is different from it being due to the inertial force acting on it from earth's rotation.

[Bored chemist]

Okay, so you are saying that the inertial force acting on every object on earth due to the earth's rotation has constant direction related to earth that results in the plumb bob to point to a displaced point in comparison to the point if earth was immobilised instead of tracing a circle.

Yes.
But the point near the Earth's centre where the plumb line points depends on the position of the pendulum.
As pointed out, it depends on latitude.
It also depends on altitude.

If this is true, then why Foucault's pendulum plane of swing rotates?

Two things
Because the latitude and altitude change, so the force changes.

Also, the plane of the pendulum of  Foucault's pendulum doesn't change.
 (in the simplest case- where it's at the pole)
If I set it swinging along the line  towards Betelgeuse it carries on swinging back and to along that line.
You don't need to account for a lack of change of motion.