People have always tried to better understand the world around them. They have described it, probed it, and theorized about it in an attempt to explain everyday phenomena. There have been many theories about the world, many of which have been wrong. For a very long time, man believed that the Earth was the center of the universe. Aristotle believed that, when dropped from the same height, a heavier object would fall to the ground faster than a lighter object. This idea was proven wrong more than 1000 years later when it was shown that, all objects, regardless of mass, fall to the ground with the same acceleration.
People throughout the ages have come up with ways to describe the world with numbers and theories. One idea that has come up over and over again is conservation: the idea that certain quantities in nature always stay the same.
Numerous quantities have been found to be conserved. Three important conserved quantities that we will be discussing are energy, linear momentum and angular momentum.
There has been no known example of a situation in which the conservation of energy, linear momentum or angular momentum does not hold true. However, from a practical standpoint, conservation is most useful when we know how to calculate and count up exactly how much of each quantity there is. We need to know how to count up how much energy, linear momentum and angular momentum there is in a system in order to use conservation to make predictions about the system.
Energy describes the nature of the system. Linear momentum is a quantity associated with motion in a straight line and angular momentum is associated with motion about a point. These three quantities are related to the state of the system. Because these quantities are conserved, we can often use them to make both general and specific predictions about how the system will behave in the future.
Conservation is all about accounting for the amounts of each quantity in every form and at every location. The theory of conservation states that we should be able to continuously account for every little bit of energy, linear momentum and angular momentum; nothing just suddenly appears or disappears. In applying the theory, we are limited by whether we can accurately measure what is there.
Often, we are only concerned with the changes in the quantities. By conservation, everything must be accounted for; an increase in one form of energy means that there was a decrease in another form. If one object gains linear momentum, another object must have lost some. In cases such as these, we are comparing the quantities before and after some interaction.
The whole idea behind conservation is that there can be no surprises. There is a source for every change. We are sometimes unable to apply conservation because we can not easily calculate the amount present of some quantity; for example, in some circumstances we might have trouble calculating heat energy. However, this does not mean that the energy is not conserved. Something else must have lost energy to produce the heat energy and it just happens that we have a hard time counting up the amount of heat energy directly. Conservation of energy, linear momentum and angular momentum is always true; we just have to be careful in how we account for the quantities that we know are conserved.
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