Change in earth's day length due to water displacement

In summary, the conversation discussed the change in Earth's day length due to the displacement of water into reservoirs. By using conservation of angular momentum and calculating the difference in moments of inertia, it was determined that the change in the day length is approximately 2.07 x 10^-4 seconds shorter.
  • #1
karnten07
213
0
[SOLVED] Change in Earth's day length due to water displacement

Homework Statement



About 10000km3 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.
[The Earth has mean density 5.5 x10^3 kgm-3, radius R = 6400km and radius of gyration
0.58R. The density of water is 1gcm-3, and, for the purposes of this question, the density
of sea water is not significantly different .

Homework Equations



i have found that radius of gyration, k has the relation k^2 = I/m


The Attempt at a Solution



i have drawn the Earth and showing the reservoirs as bulges at 45 degrees from the equators just to get an idea of what is going on. I guess i need to calculate the change in moment of inertia from no reserviors to having reservoirs at these latitudes. Then seeing how this changes the radius of gyration? Any ideas?
 
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  • #2
Okay I am confident that I've calculated the different moments of inertia of the before reserviors scenario and after reservoirs. So how can i calculate the difference in rotation period between these two different mometns of inertia?
 
  • #3
Use conservation of angular momentum: [itex]I_-\omega_- = I_+\omega_+[/itex], where the - and + subscripts denote the before reservoirs scenario and after reservoirs scenario. The rotation period is related to the angular velocity via [itex]T=2\pi/\omega[/itex].
 
  • #4
D H said:
Use conservation of angular momentum: [itex]I_-\omega_- = I_+\omega_+[/itex], where the - and + subscripts denote the before reservoirs scenario and after reservoirs scenario. The rotation period is related to the angular velocity via [itex]T=2\pi/\omega[/itex].

Brilliant, thanks for all your help guys. Out of interest, i calculated the change in the day length equals 2.07 x 10^-4 seconds shorter.
 
  • #5
You're welcome. Thread marked as 'solved'.
 

1. How does water displacement affect the length of the Earth's day?

Water displacement can affect the length of the Earth's day by changing the distribution of mass on the planet's surface. As water accumulates in certain regions, it adds weight and can cause the planet's axis to tilt slightly, resulting in a change in the Earth's rotational speed.

2. Can water displacement cause significant changes in the Earth's day length?

Yes, water displacement can cause significant changes in the Earth's day length. In extreme cases, such as a large amount of water being added to one side of the planet, the Earth's rotational speed can be altered by a few milliseconds, resulting in a slightly longer or shorter day.

3. Is water displacement the only factor that can affect the Earth's day length?

No, water displacement is not the only factor that can affect the Earth's day length. Other factors such as tectonic movements, atmospheric changes, and even human activities can also have an impact on the Earth's rotation and thus, the length of the day.

4. How do scientists measure changes in the Earth's day length due to water displacement?

Scientists use highly precise instruments such as atomic clocks and satellite data to measure changes in the Earth's day length. By monitoring the Earth's rotation and comparing it to known standards, they can accurately determine any changes in the length of the day.

5. Can changes in the Earth's day length due to water displacement have any consequences?

Yes, changes in the Earth's day length due to water displacement can have consequences, although they may be minor. For example, they can affect the Earth's climate, ocean currents, and even the length of a day on other planets in our solar system.

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