# Eotvos Exp: Gravitational v Inertial Mass Equivalence

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• Ranku
In summary, the Eotvos experiment tests the equivalence of gravitational and inertial mass by comparing the ratio of inertial forces (centrifugal force) and gravitational forces. While some descriptions state that the experiment involves the balancing of centrifugal force with gravitational force, others state that it is about providing the centripetal force. However, both are equivalent ways of describing the same phenomenon from different frames of reference. The relevant force in terms of interplay with the gravitational force is the centripetal force, which is provided by the gravity component in the inertial frame and balances the centrifugal force in the rotating frame.
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?

Ranku said:
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.

Ranku said:
The Eotvos experiment tests the equivalence of gravitational and inertial mass.
Yes
Ranku said:
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.
Ranku said:
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

A.T. said:
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?

Ranku said:
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?

A.T. said:
"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.

Ranku said:
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.

A.T. said:
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?

Ranku said:
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

## 1. What is the Eotvos Experiment?

The Eotvos Experiment is a scientific experiment that was conducted in the late 19th century by Hungarian physicist Loránd Eötvös to test the equivalence of gravitational and inertial mass.

## 2. Why is the Eotvos Experiment important?

The Eotvos Experiment is important because it provided evidence for the principle of equivalence, which states that gravitational and inertial mass are equivalent. This principle is a fundamental concept in the theory of general relativity and has implications for our understanding of gravity and the structure of the universe.

## 3. How does the Eotvos Experiment work?

The Eotvos Experiment involves measuring the difference in acceleration between two objects of different masses placed in a gravitational field. If the principle of equivalence is true, the two objects should experience the same acceleration, regardless of their mass. The experiment was able to detect a very small difference in acceleration, providing evidence for the equivalence of gravitational and inertial mass.

## 4. What were the results of the Eotvos Experiment?

The results of the Eotvos Experiment showed that the difference in acceleration between two objects of different masses was less than one part in 1011. This provided strong evidence for the principle of equivalence and supported the theory of general relativity.

## 5. How has the Eotvos Experiment been replicated?

The Eotvos Experiment has been replicated numerous times by different scientists using various methods, including torsion balances and free-fall experiments. These replications have consistently confirmed the results of the original experiment, further supporting the principle of equivalence and our understanding of gravity.

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