Group Four Project (Team 9): March 2011

Wednesday, 30 March 2011

MORE PHYSICS BEHIND THE CHANGE: Relating Radius with Period

The information presented below were all obtained from various internet sources (all of which are listed below) and this post is a compilation and a summary, in simple words for ease of understanding of the readers, of the whole process taken into consideration for the research.) Nothing has been directly pasted from a single source.

Specific to this post, its just an interpretation of the former post using physics and algebra to prove the theory right.

We can show more clearly how a change in the radius of the earth would effect the period (the length of the day) :

Photo:This photo has not been acquired from any online source and is created using Microsoft Word and Micro Soft Paint by the group.

Therefore, we can see that, a lower R(new) value will give us a lower T(new value) and vice versa. This explains how, due to the reduced radius of the earth, the length of the day, that is, the Period of the earth was also reduced.

THE PHYSICS BEHIND THE CHANGE

A quantity that can be used to describe the overall state of a physical system is said to be Angular Momentum. . Angular momentum is always conserved in a system where there is no net external moment of force.

For a rigid body rotating around an axis of symmetry (e.g. the fins of a ceiling fan, or the earth), the angular momentum can be expressed as the product of the body's moment of inertia (a measure of an object's resistance to changes in its rotation rate) and its angular velocity ω:

Photo:This photo has not been acquired from any online source and is created using Microsoft Word and Micro Soft Paint by the group.

The earth has its own Angular Momentum which is conserved. This means, that if either part of its product, i.e. the moment of inertia or the angular velocity rises, the other value of the other will fall and vice versa, in order to maintain a constant value for the Angular Momentum of the earth.

The earth can be considered a Solid Sphere, and the moment of inertia of a Solid Sphere is given by the formula :

Photo:This photo has not been acquired from any online source and is created using Microsoft Word and Micro Soft Paint by the group.

So we can say that the Earth’s Angular Momentum can be calculated by the following formula:

Photo:This photo has not been acquired from any online source and is created using Microsoft Word and Micro Soft Paint by the group.

The earthquake in Japan caused a change,a slight decrease, in the Earth’s radius as a result of the subduction of the Tectonic plates. This decrease in the radius however is very very very small in comparison to the earth’s radius before the change. This will cause the value of R in our formula will reduce. The total mass of earth still remains constant ensuring that the M value remains unchanged. Therefore, in order to keep the value of L constant (conservation of Angular Momentum), the value of the angular velocity ω will rise (by a very small amount), thus slightly speeding up the velocity at which the earth rotates and in turns shortening the 24 hour day in earth by a few micro seconds, 1.8 micro seconds to be more specific.

Picture Source: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvGGXhE2p8Gp20I_FEYH3ZiFQevkf3gNf1mNCNbzC3QZYbXqJ25m91JnP6uI79sJck1HrM4AZ4idYJ7KVFm4_r9Fq1r7Wup2sxrA8DTE80a3Q8IRLl9oejDQkOovb9UuKEcXBJzSGME-Yv/s1600/Ang_mom.gif

Source : http://en.wikipedia.org/wiki/Angular_momentum,
http://en.wikipedia.org/wiki/Moment_of_inertia.
http://hyperphysics.phy-astr.gsu.edu/hbase/isph.html

Plate Tectonics

The information presented below were all obtained fro various internet sources (all of which are listed below) and this post is a compilation and a summary, in simple words for ease of understanding of the readers, of the whole process taken into consideration for the research.) Nothing has been directly pasted from a single source.

Picture Source: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCY8FhUeignbaJAHkRlv5x3PKHJ5_03XTQQG7_U0Wb6_3b9XWeWB7VL7KByYUI5lqCEPHpCNgNH7xteZVK7l7SDt8UbZXahrt4qegX1OlskLd9cSEU_ERB4r91YEUl9LqPGeW571M6xVBk/s1600/earth-plates.jpg

Before getting into the technicalities of exactly how the earthquake caused the day to shorten we first need to obtain basic knowledge of how the earthquake was formed.

Japan is situated on the brinks of 4 plates: the Eurasian plate, the Philippine plate, the North American plate and the Pacific plate. Some earthquakes occur as a result of there being a movement between plates which makes Japan an earthquake prone island. This area is called the Pacific Ring of Fire and is the world's most active earthquake belt where rigid plates in the Earth's crust collide along the rim of the Pacific Ocean.
Source of Information :http://www.livescience.com/13187-japan-earthquake-tsunami-science-faq.html

http://www.civilengineergroup.com/earthquake-knowledge.html

The Japanese earthquake on March 11th was the result was the result of a type of converging plate boundary (subduction boundary) which is where oceanic lithosphere is pushed beneath either oceanic or continental lithosphere and in this case the denser Pacific plate was subducted under the less dense Philippine plate. It is not irregular for the Pacific Plate to move as a result of its mass and as a matter of fact it is said that it moves 3.5 inches annually. However, this move is not done gradually; at times the friction between plates causes the plate to stand at rest while building up energy so that when it finally moves the distance is greater and the force is large enough to generate an earthquake. The subduction was great enough to cause Japan to move 8 ft. eastward redistributing matter on earth and as a result it decreased the earth's radius by a minuscule amount. The following image shows what was observed of the shift of the island:
(Sources of information: http://www.livescience.com/13187-japan-earthquake-tsunami-science-faq.html

http://www.civilengineergroup.com/earthquake-knowledge.html)