Motion described in polar coordinates
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Velocity in polar co-ordinates
Equations are omitted for technical reasons - download the original pdf
The position of a particle at a point P in polar co-ordinates is [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 P from the origin. The velocity is [Equation goes here - download the original to see it.] So the radical component of the velocity is and the transverse component is. [Equation goes here - download the original to see it.] are perpendicular to one another (they are "orthogonal") [Diagram goes here - download the original to see it.] Hence, the speed, , of a particle is given by [Equation goes here - download the original to see it.] Example In one of Jules Verne's books a space craft in the form of a giant cannon ball is launched from a huge cannon. At the moment of launch, the cannon ball, containing three brave men, has radical speed [Equation goes here - download the original to see it.]. The period of the earth's rotation on its own axis of revolution is 24 hours and its radius is 6,380 km. Find the speed at which our three intrepid explorers are travelling at the instant at which the cannon ball leaves the cannon. Solution The period is [Equation goes here - download the original to see it.] The angular velocity is [Equation goes here - download the original to see it.] The transverse component of the velocity is [Equation goes here - download the original to see it.] The radial speed is [Equation], hence the speed is [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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