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Vectors (Knight: 3.1 to 3.4)
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Scalars and Vectors Temperature = Scalar
Quantity is specified by a single number giving its magnitude. Velocity = Vector Quantity is specified by three numbers that give its magnitude and direction (or its components in three perpendicular directions).
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Properties of Vectors Two vectors are equal if they have the same magnitude and direction.
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Adding Vectors
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Subtracting Vectors
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Combining Vectors
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Using the Tip-to-Tail Rule
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Clicker Question 1 Question: Which vector shows the sum of A1 + A2 + A3 ?
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Multiplication by a Scalar
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Coordinate Systems and Vector Components
Determining the Components of a Vector The absolute value |Ax| of the x-component Ax is the magnitude of the component vector . The sign of Ax is positive if points in the positive x-direction, negative if points in the negative x-direction. The y- and z-components, Ay and Az, are determined similarly. Knight’s Terminology: The “x-component” Ax is a scalar. The “component vector” is a vector that always points along the x axis. The “vector” is , and it can point in any direction.
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Determining Components
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Cartesian and Polar Coordinate Representations
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Unit Vectors Example:
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Working with Vectors ^ A = 100 i m
B = (-200 Cos 450 i Cos 450 j ) m = (-141 i j ) m ^ ^ ^ ^ C = A + B = (100 i m) + (-141 i j ) m = (-41 i j ) m ^ ^ ^ ^ C = [Cx2 + Cy2]½ = [(-41 m)2 + (141 m)2]½ = 147 m q = Tan-1[Cy/|Cx|] = Tan-1[141/41] = 740 Note: Tan-1 Þ ATan = arc-tangent = the angle whose tangent is …
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Tilted Axes Cx = C Cos q Cy = C Sin q
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Arbitrary Directions
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Perpendicular to a Surface
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Chapter 3 Summary (1)
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Chapter 3 Summary (2)
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