Chapter 03a - Chapter 3A Vector Quantities Vector...

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Chapter 3A 1 Vector Quantities Vector quantities are characterized by having both a magnitude, with appropriate units, and a direction. By contrast, scalar quantities have a magnitude, but no direction. vectors displacements velocities accelerations forces scalars time intervals lengths areas volumes
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Chapter 3A 2 A = 5.00 m θ A = 36.9 ° + x + y Vector Quantities r A A or Vector quantities are represented graphically with arrows, and in text with bold-faced type: In this example, A is a displacement vector. Its magnitude is 5.00 m; its direction is 36.9 ° above the + x axis.
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Chapter 3A 3 A θ A + x + y A y A x Vector Components Vectors can be resolved into components that line up with the coordinate axes. A vector’s “ x component” is its projection onto the x axis. A vector’s “ y component” is its projection onto the y axis. ( θ must be relative to the + x axis.) A x = A cos θ A A y = A sin θ A
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Chapter 3A 4 A = 5.00 m θ A = 36.9 ° + x + y A y = 3.00 m A x = 4.00 m Vector Components This means that displacement vector A extends 4.00 m in the + x direction and 3.00 m in the + y direction. A y = A sin θ A A y = (5.00 m)(sin 36.9 o ) A y = 3.00 m A x = A cos θ A A x = (5.00 m)(cos 36.9 o ) A x = 4.00 m If: A = 5.00 m θ A = 36.9 °
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Chapter 3A 5 Vector Addition Vectors of the same type can be added graphically or mathematically.
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