Movement of Water - Increasing day length

[Sekonda]

Hey,

I have a problem which I'm having trouble solving, it concerns the conservation of angular momentum.

I am given a volume of water that is held behind dams in the mid-latitudes on the Earth and am asked to determine the change in length of the day due to the movement of the water into these reservoirs. The water is moving from the equator, I believe, into these mid latitude based reservoirs. I am given the radius of gyration, radius and density of the Earth, I am still unsure what exactly the radius of gyration is! I am also told the density of water.

Now the problem is solved by using conservation of angular momentum; now what I think I have to do is find the angular momentum about a diameter axis of the Earth initially with its initial angular velocity and then to equate this to the sum of the angular momentum of the Earth about the same axis with its final angular velocity, and the angular momentum of the water in its new location.

I'm not sure if this is correct, and I'm a bit confused of how to formulate the last term - the angular momentum of the water in its new location.

Thanks for any help guys!
S

 

[Sekonda]

I'll try and simplify my questions!

What exactly is the radius of gyration and how is it applicable to a rotating (around a diameter fixed axis) solid spherical mass in which a small amount of mass, equally distributed around the equator, is moved to the mid-latitudes, I'm guessing 45 degrees.

I think this is at the heart of my issue with this particular problem, thanks guys!

 

[qazxsw]

i'd give it a go for a random guess at about 0.2ms

hope this helps a lot:)