L5-Vectors

L5-Vectors - Vectors: Motion/Forces/Momentum Prof. John...

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Vectors: Motion/Forces/Momentum Prof. John Conway Physics 7B - Lecture 5
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Vectors Defined A vector is a mathematical object which has magnitude (length) direction We often represent a vector by drawing an arrow:
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Vectors Defined A vector does not have a position in space! These two vectors are the same since they have the same direction and magnitude:
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Vectors are Useful We can use vectors to represent position in space velocity forces fields (electric, magnetic, . ..) what else?
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Not a Vector - PRS Of the following which can not be represented by a vector? A.gravitational force B. wind velocity C.fluid pressure D.location in 3D space E. magnetic field
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Representing Vectors Let’s start with a two-dimensional vector which is five units in magnitude, and oriented at an angle of 53.1 degrees from horizontal y 3 units 4 units What are the funny things with hats??
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Representing Vectors A vector is expressed in a particular coordinate system (also called “basis”) We often use Cartesian coordinates (x,y,z) as the basis for vectors Coordinate system has origin, scale, orientation, and “handedness” To understand how to write vectors, though, we need to first understand how to scale and add them!
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Scaling Vectors Scaling a vector (multiplying it by a real number) makes it either longer or shorter: B _ B _ 2 B _ 0.6 Scaling a vector does not change its direction!
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It isn’t obvious at first how vectors add toghether! + = A
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L5-Vectors - Vectors: Motion/Forces/Momentum Prof. John...

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