Motion described in polar coordinates
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Motion described in polar coordinates. Vectors in polar co-ordinates
Suppose a particle at point [Equation goes here - download the original to see it.] - that is a particle whose position is given in polar co-ordinates - has velocity v. The velocity can be described in terms of its radical and the transverse components [Diagram goes here - download the original to see it.] In order to do so we define to be a unit vector in the radical direction and [Equation goes here - download the original to see it.] to be a unit vector in the transverse direction - that is, perpendicular to [Equation goes here - download the original to see it.] and taken in an anti- clockwise direction. [Diagram goes here - download the original to see it.] So the velocity is [Equation goes here - download the original to see it.] where [Equation goes here - download the original to see it.] are the magnitudes of the radical and transverse components respectively. The position of the particle at can also be given in these polar vectors. [Equation goes here - download the original to see it.] where [Equation goes here - download the original to see it.] is the magnitude of the distance of [Equation goes here - download the original to see it.] from the origin. If an object is moving in a circle with centre and radius , then its position is [Equation goes here - download the original to see it.] and its velocity is [Equation goes here - download the original to see it.] its acceleration is [Equation goes here - download the original to see it.] that is its acceleration is directed along the radius towards the centre.
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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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