Cavendish experiment to determine G

[SuchBants]

I'm doing the experiment for a project using a setup as so:
https://imgur.com/a/7vfg2
In the derivation of the formula I used the amplitude of the oscillation on the ruler of the laser, basically taking it as the arclength of the arc drawn by the laser spot as the bar rotates inside the apparatus and got the same formula as given to me by an instructor:
https://imgur.com/a/ynAlx
He has written the value I used as the arclength of the laser as the "difference of scale readings of the equilibrium positions of the spot corresponding to the two arrangements (A) and (B) "

Positions A and B being the two possible positions of the large spheres.

Can anyone explain what this means? Why is there a difference between the equilibrium positions and how does that equal the arclength the laser draws out?

 

[kuruman]

Imagine the large spheres oriented in an intermediate position between (A) and (B) so that their supporting rod is perpendicular to the rod supporting the small spheres (see below left). In this case, because of symmetry, the net torque on the small sphere assembly is zero. When you rotate the large sphere assembly so that A gets closer to the small sphere on the left and B gets closer to the small sphere on the right (see below right), will the small sphere assembly rotate or not? If so, in what direction, clockwise or counterclockwise? What about if the large spheres are rotated the other way?

 

[SuchBants]

Imagine the large spheres oriented in an intermediate position between (A) and (B) so that their supporting rod is perpendicular to the rod supporting the small spheres (See below left). In this case, because of symmetry, the net torque on the small sphere assembly is zero. When you rotate the large sphere assembly so that A gets closer to the small sphere on the left and B gets closer to the small sphere on the right, will the small sphere assembly rotate or not? If so, in what direction, clockwise or counterclockwise? What about if the large spheres are rotated the other way?

View attachment 220119

So the small balls would rotate clockwise initially, then anticlockwise due to the restoring torque which gives it its oscillatory motion. And the reverse would happen if the large balls were in the other position.
I can picture that this would produce two arcs where the equilibrium positions are separated but can't understand how the difference of the equilibrium positions fits in...

 

[kuruman]

The oscillations are useful in finding the period which can be linked to the torsional constant of the filament suspension. Eventually, the amplitude of the oscillations will die out regardless of which configuration the large spheres are in. If the "zero" (no gravitational force) is when the supporting rods are perpendicular, then the effect of gravity can be calculated by measuring the angular displacement Δθ of the equilibrium position when the large spheres are brought closer than the perpendicular or zero configuration. If you think a bit about it, you will see that the difference between the equilibrium positions is 2Δθ. Considering how small Δθ is, you get better accuracy by measuring twice that much.

 

[SuchBants]

I think I've understood it now. Ignoring the oscillations as just a result of it being a twisting of a wire, then the wire rotates θ to the rest position due to the gravitational attraction of the two large spheres. And it rotates θ to the other rest position when the balls are moved - therefore the difference in the rest positions being 2θ. Thank you!

 

[kuruman]

I think I've understood it now.

Yes you have.