How Do Large Water Reservoirs Effect The Length of the Day

[alex3]

Homework Statement

Verbatim from the problem:

"About $$10000km^3$$ of water is held behind dams in reservoirs around the world.Most reservoirs are at mid-latitudes, whilst the bulk of the world’s oceans are concentrated near the equator. By using conservation of angular momentum, estimate by how much the overall movement of water into reservoirs has changed the length of the day."

Homework Equations

$$r^{2}_{g} = \frac{I}{M}$$
$$\rho_E = \frac{M}{V}$$
$$V = \frac{4}{3} \pi R^{3}_{E}$$
[tex]L = I\omega = r^{2}_{g} M\omega[\tex]

The Attempt at a Solution

 

[jbsteele]

Based on the equation, L = Iω, where I is the moment of inertia and ω is the angular velocity, the conservation of angular momentum must be used to calculate the change in length of the day. To do this, I must first be calculated.I can be calculated using the equation I = Mr2g, where M is the mass of the water and rg is the radius of gyration. The mass of the water can be calculated using the equation ρE = M/V, where ρE is the density of the Earth and V is the volume of the water. The volume of the water can be calculated from the given data, which is 10,000km3. The density of the Earth can be found from a quick Google search and is 5.515 g/cm3. Once the mass of the water is calculated, the radius of gyration can be calculated. This can be done by calculating the radius of the Earth, which is 6,378 km, and then dividing it by the square root of 2. With I and ω known, the equation L = Iω can then be used to calculate the change in the length of the day. The calculated change in the length of the day is approximately 0.3 milliseconds.