Motion described in polar coordinates
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Rate of change of radial direction and radial angle
A unit vector in the radial direction is [Equation goes here - download the original to see it.] Suppose [Equation goes here - download the original to see it.] is in fact a function of another parameter for example could represent time. Then [Equation goes here - download the original to see it.] would give the position of the radial vector at time . [Diagram goes here - download the original to see it.] Then [Equation goes here - download the original to see it.] Using the chain rule [Equation goes here - download the original to see it.] since [Equation goes here - download the original to see it.] then [Equation goes here - download the original to see it.] so [Equation goes here - download the original to see it.] where [Equation goes here - download the original to see it.] The rate of change of [Equation goes here - download the original to see it.] is in the [Equation goes here - download the original to see it.] direction and has magnitude [Equation goes here - download the original to see it.] We use the same approach to find the rate of change of [Equation goes here - download the original to see it.] [equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] Therefore [Equation goes here - download the original to see it.]
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Contents of
Motion described in polar coordinates
1 Motion described in polar coordinates. Vectors in polar co-ordinates
2 Change of basis
3 Rate of change of radial direction and radial angle
4 Velocity in polar co-ordinates
5 Acceleration in polar co-ordinates
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