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## Main Question or Discussion Point

*I don't know if this belongs to homework section or not.

I just found the description in my book interesting and want to know more. If this is inappropriate, please move it to homework section.

Compton Generator is basically a device invented by Compton which is used to measure the Coriolis Force (a fictitious force in non-inertial frame). As described in my physics book, it works like this:

First, you get a torus filled with water and flat on the ground (the water is initially non-rotating in the frame of the earth), then you flip the device 180 degrees through the east-west axis.

My physics book claims that after the flip, the water in the torus begins to rotate. The book even gives a explicit formula for the speed after the flip, which is only dependent on the radius of the torus and the colatitude (assuming the cross section of the torus is very very small comparing to the torus as a whole).

my understand of how the device works is that when one turns the torus, the water gains velocity in the turning direction. The Coriolis Force then changes the direction of that vector, resulting in a net tangential velocity.

The device seems very interesting... and I've been trying to figure out the mathematics behind it... I tried to assume constant angular velocity when flipping the torus, but that integral turns out quite messy and is dependent on the angular velocity. I couldn't find any work-energy relationship either, since Coriolis Force is absolutely non-conservation.

there might be some kind of parallelism between magnetic flux and this. But that seems to be true only if an initial "current" (flow of water) is presented (similar to how energy is magnetic moment dot magnetic field). I can express the torque in terms of the flow in the torus, radius and such but that doesn't seem to help much (since it is dependent on the flow/speed of the water)

The speed of the water after 180 flip is as following:

[tex]v=2\Omega R \cos\theta[/tex]

where Omega is the angular velocity of the earth, theta is the colatitude.

I wonder if the equation in my book really works. And what about the equation for speed for turning any amount of degrees (v in terms of the angular displacement). And what happen if the shape is not a torus, but a random closed loop (smooth) of water? And what if you turn the torus the other way around 180 degrees? (I suppose the water will stop rotating)

I just found the description in my book interesting and want to know more. If this is inappropriate, please move it to homework section.

Compton Generator is basically a device invented by Compton which is used to measure the Coriolis Force (a fictitious force in non-inertial frame). As described in my physics book, it works like this:

First, you get a torus filled with water and flat on the ground (the water is initially non-rotating in the frame of the earth), then you flip the device 180 degrees through the east-west axis.

My physics book claims that after the flip, the water in the torus begins to rotate. The book even gives a explicit formula for the speed after the flip, which is only dependent on the radius of the torus and the colatitude (assuming the cross section of the torus is very very small comparing to the torus as a whole).

my understand of how the device works is that when one turns the torus, the water gains velocity in the turning direction. The Coriolis Force then changes the direction of that vector, resulting in a net tangential velocity.

The device seems very interesting... and I've been trying to figure out the mathematics behind it... I tried to assume constant angular velocity when flipping the torus, but that integral turns out quite messy and is dependent on the angular velocity. I couldn't find any work-energy relationship either, since Coriolis Force is absolutely non-conservation.

there might be some kind of parallelism between magnetic flux and this. But that seems to be true only if an initial "current" (flow of water) is presented (similar to how energy is magnetic moment dot magnetic field). I can express the torque in terms of the flow in the torus, radius and such but that doesn't seem to help much (since it is dependent on the flow/speed of the water)

The speed of the water after 180 flip is as following:

[tex]v=2\Omega R \cos\theta[/tex]

where Omega is the angular velocity of the earth, theta is the colatitude.

I wonder if the equation in my book really works. And what about the equation for speed for turning any amount of degrees (v in terms of the angular displacement). And what happen if the shape is not a torus, but a random closed loop (smooth) of water? And what if you turn the torus the other way around 180 degrees? (I suppose the water will stop rotating)

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