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Tutorial Ten: Introduction to Theories of Motion

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Physics is an extremely exciting field. However, its elegance is often hidden behind a wall of mathematics that masks its simplicity and beauty. Fortunately, some aspects of physics, even those that seem complex, can be explained using easy to recognize ideas and concepts. You might be surprised to learn that in the first nine entries of this tutorial series, we’ve already […]

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Tutorial Nine: How things move (Part 4)

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This is our fourth and final tutorial on how things move. In tutorials six and seven, we explored how things move and change position. In Tutorial eight, we looked at how far something moves. In this tutorial, we are going to take what was introduced in the previous tutorials to explore solving a question involving distance and position. We’re […]

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Tutorial Eight: How things move (Part 3)

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Tutorials six and seven introduced the translation transformation, also called the Newtonian equation. The Newtonian equation, which forms the foundation of classical mechanics is extremely useful and describes how objects move from one place to another. Answering questions about positions is extremely useful. Modern Mechanics, a model we’ll introduce shortly as a superset of classical mechanics and a replacement […]

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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 […]

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Tutorial Two: Averages… the easy way

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The average height of an American male is 5’10”. The average height of an American female is 5’5”. The average price of a home sold in the United States in 2010 was $272,900. We use averages all the time.  In fact, the average is one of the most widely used tools in mathematics. It is […]