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Lecture 1 - Vectors
Course: PH 1110, Spring 2008School: WPI
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Notes PH1110 Vectors Ch 1 Sec 7,8,9 1.7 Vectors and Vector Addition Velocity has a speed and a direction Scalar Quantity- when a physical quantity is described by a single number Vector Quantity- has both a magnitude (the "how much" or "how big" part) and a direction in space. Displacement- is simply a change in position of a point Vectors are in boldface italic type with an...
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Notes PH1110 Vectors Ch 1 Sec 7,8,9
1.7 Vectors and Vector Addition
Velocity has a speed and a direction Scalar Quantity- when a physical quantity is described by a single number Vector Quantity- has both a magnitude (the "how much" or "how big" part) and a direction in space. Displacement- is simply a change in position of a point Vectors are in boldface italic type with an arrow above them If 2 vectors have the same direction they are parallel, if they have the same direction and magnitude they are equal. Negative of a vector- when vectors have the same magnitude but opposite direction Anti-Parallel Vectors- when two vectors have opposite directions, whether their magnitudes are the same or not. Magnitude is represented by light italic type with no arrow on top The magnitude of a vector quantity is a scalar quantity and is always positive Vector Addition Vector Sum / Resultant- distance from origin to final point Vector addition can be done by means of the head to tail method where you place the tail of the second vector at the head of the first vector. The sum of the vectors is the distance from the origin (tail of the first vector) the to head of the second vector. Vector subtraction can be done just as vector addition but one of the vectors must become the negative of its former self.
1.8 Components of Vectors
Component Vectors- breaking up any vector on the x/y coordinate system into both of its x and y components. Clockwise rotation on the coordinate system is a negative angle Counter-Clockwise rotation on the coordinate system is a positive angle Doing Vector Calculations Using Components Pythagorean theorem can be used to find the components of the vectors Vectors can be multiplied by scalars such as vector a multiplied by 2 is 2a Adding or subtracting vector components can lead to the sum or resultant of two or more vectors leading in a more practical approach then the head to tail method
1.9 Unit Vectors
Unit Vector- is a vector that has a magnitude of 1, with no units. Its only purpose is to point that is to describe a direction in space. Unit vectors have carets of "hats" (^) to distinguish them from ordinary vectors. I,J,K notation is used o I "hat" for the x direction o J "hat" for the y direction o K "hat" for the z direction
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