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Tutorial Six: How things move (Part 1)

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One of the most interesting aspects of physics is that it helps to describe how things move.  This characteristic builds upon a mathematical foundation called geometric transformations.  While this name, geometric transformation, sounds complicated, some of its most important ideas are actually quite easy to explain. Imagine for a moment that you need to open […]

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Tutorial Five: How Einstein finds an average

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Now that you’ve been introduced to averages and Doppler equations, let’s combine these two ideas. This will also give us an opportunity to start looking at Einstein’s theory of relativity. We’ll begin with a few questions and answers: Do you need relativity theory to find the average of two numbers? Answer: No, you do not need relativity theory […]

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Tutorial Four: Trains and the Doppler effect

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The Doppler effect (also called Doppler shift) is one of the most widely–observed phenomena associated with moving objects. In fact, we often observe it when we hear the sound coming from moving vehicles like cars, trucks, and trains.  Imagine that a tape recorder is placed on a railroad track. The recorder’s microphone records the sound of the […]

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Tutorial Three: Averages… Part 2!

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Averages are extremely powerful mathematical tools.  In the previous tutorial, you were introduced to the addition mean equation, which is used to find the average (or arithmetic mean) of two numbers. Most people automatically use the addition mean equation when asked to find the average of two numbers. But, did you know that there is another novel way to find […]