Eotvos Exp: Gravitational v Inertial Mass Equivalence

[Ranku]

The Eotvos experiment tests the equivalence of gravitational and inertial mass. Some descriptions state that the experiment tests the equivalence between gravitational and centrifugal force, while others state that it is between gravitational and centripetal force. There is a significant difference between the two: Centrifugal force is a fictitious force, like inertial force, and its cancellation with gravitational force would require that the two masses in the torsion balance must be effectively in gravitational freefall. Centripetal force is a real force, and its balancing would require that the two masses not be in freefall and experience the gravitational force. So does the experiment involve centrifugal or centripetal force?

 

[jbriggs444]

The Eotvos experiment tests the equivalence of gravitational and inertial mass. Some descriptions state that the experiment tests the equivalence between gravitational and centrifugal force, while others state that it is between gravitational and centripetal force. There is a significant difference between the two: Centrifugal force is a fictitious force, like inertial force, and its cancellation with gravitational force would require that the two masses in the torsion balance must be effectively in gravitational freefall. Centripetal force is a real force, and its balancing would require that the two masses not be in freefall and experience the gravitational force. So does the experiment involve centrifugal or centripetal force?

If you set out to measure centrifugal force, how would you go about it?

You could set up a rotating coordinate system and an apparatus that is rotating along with the coordinate system. You could verify the rotation rate, the axis of rotation and the displacement of a test object from that axis. You could then use a strain gauge to determine the centripetal force required to hold the test object stationary relative to the apparatus.

Having done this, are you measuring centripetal force or centrifugal force? Six of one, half dozen of the other. If the two are equal by construction, it does not matter which one you think you are measuring.

 

[A.T.]

The Eotvos experiment tests the equivalence of gravitational and inertial mass.

Yes

Some descriptions state that the experiment tests the equivalence between gravitational and centrifugal force, while others state that it is between gravitational and centripetal force.

Both is not quite accurate. It's about the ratio of inertial forces (here centrifugal) versus the ratio of gravitational forces.

Centrifugal force is a fictitious force, like inertial force, and its cancellation with gravitational force...

They aren't cancelling. Read the wiki and look at the diagram:
https://en.wikipedia.org/wiki/Eötvös_experiment

 

[Ranku]

They aren't cancelling. Read the wiki and look at the diagram:
https://en.wikipedia.org/wiki/Eötvös_experiment

After reading in the textbook that centripetal force is involved, I got confused reading in wiki that centrifugal force is involved. That's why I asked for clarification, how can both be correct?

 

[A.T.]

After reading in the textbook that centripetal force is involved, I got confused reading in wiki that centrifugal force is involved. That's why I asked for clarification, how can both be correct?

"Is involved" is very vague. What does it say exactly?

 

[Ranku]

"Is involved" is very vague. What does it say exactly?

This is the passage from the book Gravity by Hartle (pp.108):
Imagine two masses of different material at the ends of a rod that is suspended from a fibre in a laboratory on the surface of the earth. Because the laboratory is rotating with the Earth, the hanging fibre is not exactly aligned with the local force of gravity. Rather, the fibre hangs at a small angle to that direction so that a small component of the gravitational force can balance the centripetal acceleration arising from the Earth's rotation.
The masses are free to move in the direction perpendicular to both the fibre and the rod. Gravity is the only force acting in the 'twisting direction' along which the masses effectively freefalling. Any difference between the accelerations of the two masses would cause the pendulum to twist. Thus, a difference in the equality of their gravitational and inertial masses could be detected.

 

[A.T.]

This is the passage from the book Gravity by Hartle (pp.108):
... a small component of the gravitational force can balance the centripetal acceleration arising from the Earth's rotation...

This would be better stated as: "... can provide the centripetal force ..." and is equivalent to saying: " ... can balance the centrifugal force ...", just described from the inertial frame, instead of the rotating frame.

 

[Ranku]

This would be better stated as: "... can provide the centripetal force ..." and is equivalent to saying: " ... can balance the centrifugal force ...", just described from the inertial frame, instead of the rotating frame.

So what's the relevant force in terms of interplay with the gravitational force - is it the centripetal or centrifugal force?

 

[A.T.]

So what's the relevant force in terms of interplay with the gravitational force - is it the centripetal or centrifugal force?

Inertial frame: Gravity component provides centripetal force
Rotating frame: Gravity component balances centrifugal force