The velocity of the particle is easily found by differentiationĬheck that this is perpendicular to the position vector of the particle by taking the scalar product of the two vectors. Hence we find for the cartesian coordinates If a particle is going round a circle with a constant angular speed, integrating the above equation gives The SI units of ω are radians per second. Having defined angular position it is also useful to define the corresponding angular speed, θ therefore defines the angular position of the rotating particle. The characteristic feature of circular motion is that the radius is fixed and only the angle θ moves as time proceeds. (If you are in doubt, remember that a full circle is 2π radians and that the circumference is 2π r. If θ is measured in radians, then the distance travelled by the particle from the x axis, measured round the arc of the circle is s = rθ. It is much more convenient to use polar coordinates, r representing the distance to the centre of the circle and θ representing the angle measured anticlockwise from the x axis. Which has an unfortunate ambiguity of sign. We can use Cartesian coordinates, but these are not very convenient, the relationship between x and y on a circle of radius r is We first need a way of defining the position of a particle in its circular motion. We initially start with this simplified version, but it will need to be generalised because some problems in chemistry require a more sophisticated analysis. This topic deals with a single mass performing a circular motion.
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