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| course_planning:course_notes:vectors [2014/06/18 16:12] – [Vector Simulation] caballero | course_planning:course_notes:vectors [2014/06/18 17:01] (current) – [Definitions] caballero |
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| **Scalars:** Quantities that can be represented by a single number. Typical examples include mass, volume, density, and speed. | **Scalars:** Quantities that can be represented by a single number. Typical examples include mass, volume, density, and speed. |
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| {{ course_planning:course_notes:basic_vector.jpg?200|Basic Vector Diagram}} | {{ course_planning:course_notes:basic_vector.png?200|Basic Vector Diagram}} |
| **Vectors** Quantities than have both a magnitude and direction. Typical examples include displacement, velocity, momentum, and force. | **Vectors** Quantities than have both a magnitude and direction. Typical examples include displacement, velocity, momentum, and force. |
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| Vectors are often represented with arrows. The end with the triangle is the "tip" or "head". The other end is called the "tail". The tail of a vector can be located anywhere; it is the difference between the tip and the tail that defines the vector itself. | Vectors are often represented with arrows. The end with the triangle is the "tip" or "head". The other end is called the "tail". The tail of a vector can be located anywhere; it is the difference between the tip and the tail that defines the vector itself. To the right is an example of a typical representation of a vector with the tip and tail labeled. |
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| ==== Defining Vectors Mathematically ==== | ==== Defining Vectors Mathematically ==== |
| For subtraction, draw the vector that points directly opposite of the second vector. Place the tail of this reversed second vector at the tip of the first vector. The vector that points from the tail of the first to the tip of the reversed second is the difference vector. The image to the right demonstrates this for two vectors, $\vec{a}$ and $\vec{b}$. | For subtraction, draw the vector that points directly opposite of the second vector. Place the tail of this reversed second vector at the tip of the first vector. The vector that points from the tail of the first to the tip of the reversed second is the difference vector. The image to the right demonstrates this for two vectors, $\vec{a}$ and $\vec{b}$. |
| ==== Vector Simulation ==== | ==== Vector Simulation ==== |
| Here's simulation that let's you play with vectors in 2D. If the embedded simulation doesn't work, you can find it {{http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html|on the PhET website}}. | Here's simulation that let's you play with vectors in 2D.((Credit the {{http://phet.colorado.edu|PhET Team}} at the University of Colorado for the simulation.)) If the embedded simulation doesn't work, you can find it {{http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html|on the PhET website}}. |
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| {{url>http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html 800px,600px | PhET Vector Simulation}} | {{url>http://phet.colorado.edu/sims/vector-addition/vector-addition_en.html 800px,600px | PhET Vector Simulation}} |