© brenda yasie lee functions, variables, and constants...© brenda yasie lee example #1. a sphere...

© Brenda Yasie Lee

1.2 Functions, Variables, and Constants

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1.3 Visualization of Functions

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1.4 Vectors and Unit Vectors

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1.5 Vector Products: The Dot Product

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1.8 Coordinate Systems: Cylindrical Coordinates

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1.9 Coordinate Systems: Spherical Coordinates

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Example #1. A sphere of radius has a mass with density linearly changing with radius, such that the density is 0 at thecenter of the sphere. Calculate the density as a function of radius.

1.10 Examples and Important Integrals

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Example #2. The density of a sphere varies as sin . Calculate the total mass.


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Example #4. Calculate the moment of inertia of a sphere of mass and radius rotating about the axis shown in thefigure below. The sphere has uniform density.


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Example #5. An Archimedes' spiral is the trajectory of a point moving uniformly on a straight line of a plane while the lineturns itself uniformly around one of its points. An example is the rotation of the stylus on a good old vinyl disk. The curveof one type of an Archimedes' spiral is given by the mathematical function , where is the radius from theorigin and is the angle the line makes with the axis. Let us calculate the following parameters for one turn(that is changes from 0 to 2 ):

The circumference of the curve1.The area enclosed within the curve2.


© brenda yasie lee functions, variables, and constants...© brenda yasie lee example #1. a sphere...

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