Motion-Momentum - Physical Sciences 2 Reading for Thursday...

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Physical Sciences 2 Reading for Thursday, Sept. 10 Motion and Momentum Life involves motion . This motion takes place on many size scales: from the motion of an entire organism, to the motion of a single cell, to the motion of an electron in a molecule. Even stability or equilibrium ultimately involves the concept of motion, for it is only in response to motion that we can know if a system is in a state of stable equilibrium. The motion of molecules, cells, and organisms (but not electrons!) can all be described using the branch of physics known as Newtonian Mechanics, which was developed by Isaac Newton in his Principia Mathematica of 1687. In this course, we will study many applications of mechanics to biological systems. In physics, the concept of motion is linked with the concept of momentum. In everyday speech, we say that something has “momentum” if it has a tendency to continue or progress. Here are several recent headlines from the New York Times that include the term “momentum”: With Surge in Momentum, Obama Makes His Case Project to Power Europe With Sahara Sun Gains Momentum Momentum Propels Gold Over $1,000 Democrats Seek to Keep Momentum Going in the West In physics, whenever an object is in motion, that object has momentum . One of the most important laws in physics is the Law of Conservation of Momentum, which states that: Momentum is Conserved . This statement of the Law of Conservation of Momentum is not very useful yet, since we haven’t defined either “momentum” or “conserved.” Indeed, the definition of “momentum” has changed several times in the history of physics: first in 1905, with Einstein’s Special Theory of Relativity, and then again in the 1920’s, with the development of quantum mechanics. Even the definition of “conserved” changed in 1915 with Einstein’s General Theory of Relativity. Nevertheless, every successful physical theory since the time of Newton has had something called “momentum” that is always “conserved.” As far as we know, this conservation law is exact: no violations of the Law of Conservation of Momentum have ever been observed. Our task over the next week is to explore the meaning and utility of this fundamental law.
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2 The Momentum of a Single Object You may be familiar with the definition of momentum in Newtonian mechanics: if an object with mass m is moving with velocity ! v , then the object has a momentum ! p given by the expression: ! p = m ! v The momentum of an object belongs to that object; each object “owns” its own momentum. Indeed, you should think of the momentum of an object as located inside that object. You will not be led astray if you conceive of momentum as something tangible that is possessed by any object that is in motion. The above equation—the definition of momentum—is a
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Motion-Momentum - Physical Sciences 2 Reading for Thursday...

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