ROTATIONAL DYNAMICS Uniform circular motion. THE RADIAN
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The radian is a measure of angle, 1 radian is equal to the angle swept out by a chord of length equal to the radius, hence as the total circumference of the circle is equal to π multiplied by the diameter, a complete circle is 2 π radians. Radians have no dimensions. |
ANGULAR VELOCITY
The angular speed of a body is the number of radians turned through per second. It is often given the symbol ω (omega).
The dimensions of angular speed are [M]0 [L]0 [T]-1. Particles
travelling with the same angular speed (ω) will not always have the same instantous velocity at the same point on their circular
path, a particle travelling in a larger radius will have to travel faster to cover the same angle. For a general body, the time to travel though a complete
circle will be 2 π / ω and the actual distance they will have travelled 2 π r, hence the
speed of the particle is equal to ω r, the angular speed multiplied by the radius. The angular velocity is also know as the angular frequency.
