2053Lecture2

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Unformatted text preview: on To construct coordinate systems, we define the To Cartesian product of two sets X and Y as the set X × Y = {(x, y)| x∈X, y∈Y}. With R denoting With {( )| the set of real numbers, we construct some familiar coordinate systems: familiar The two–dimensional Cartesian coordinate system, dimensional called the real plane R2, is defined by the set R × R = {(x, y)| x∈R, y∈R}. {( )| The three–dimensional Cartesian coordinate system, dimensional called the real three–dimensional space R3, iis s called dimensional defined by the set defined R × R × R = {(x, y, z)| x∈R, y∈R, z∈R}. {( )| Scalars Scalars A physical quantity that has the same physical value in any coordinate system is called a scalar. We write a scalar as the product scalar We of a numerical value and a physical unit, not just a number. For example, the distance between two points is 5.3m or the 5.3 temperature of the room is 76º Celsius. 76 2–Dimensional Vectors Recall that we can write a location in the xy– Recall xy plane as the point (Ax, Ay). A 2–dimensional plane dimensional vector A = <Ax, Ay> = Ax î+ Ay ĵ = A @ θ is a vector <A physical quantity that has both magnitude and direction, where the vectors î = <1,0>...
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This note was uploaded on 02/10/2010 for the course PHY 2053 taught by Professor Hardy during the Spring '10 term at University of Southern Maine.

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