2-Vectors - AME 352 VECTORS Vectors Vectors Vectors are...

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AME 352 VECTORS P.E. Nikravesh 1 Vectors Vectors Vectors are denoted by bold-face characters such as R , V , etc. The magnitude of a vector, such as R , is denoted as: | R | , R , or R The angle of a vector is denoted as ± which is measured positively (CCW) with respect to the positive x -axis, as shown for four different vectors. In kinematics and dynamics a vector may represent position, velocity, acceleration, or force/moment. R V F A Note : When you write by hand, since you cannot write in boldface, denote a vector with an over-score arrow or an underline, for example ± R or R . Types of Vectors Position Vector A position vector connects two points. Both points could be moving, such as R BA , or both could be stationary, or one point moving and one stationary, such as R CO , where O is a stationary point. Note : A point that is represented as a small black circle is assumed stationary (defined on the ground or attached to the frame). A B R BA O C R CO Rotated Vector A position vector R if rotated 90 ± CCW will be represented as ± R . The rotated vector will have the same magnitude as R . This notation will become useful later on in representing some velocity and acceleration vectors. R ± R Velocity Vector The time derivative of a position vector yields the velocity of that vector. For example: d dt R BA = V BA , d dt R CO = V CO These vectors are read as the velocity of B relative to A
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This note was uploaded on 09/08/2010 for the course AME 352 taught by Professor Nikravesh during the Fall '08 term at University of Arizona- Tucson.

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2-Vectors - AME 352 VECTORS Vectors Vectors Vectors are...

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