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Angles and angular velocities
Radians are more fundamental units of angle than degrees. The definition of a degree is arbitrary:
1/360th of a full circle turn. In radians an angle is defined by:
Angle (rad) = arc length / radius
Since the circumference of a circle is 2r, there are 2 radians in one full revolution.
2 radians = 360° = 1 revolution
Measuring angles in radians has the additional benefit that for small angles
Sin = tan = in radians
Uniform circular motion and angular velocity
Uniform circular motion is simply motion along a circular path at a constant speed. If the
period is T, speed v is given by:
V = 2r/t
Angular velocity is rate of change of angular displacement a measure of rate of rotation.
Angular velocity is usually denoted by the Greek letter . It's units are rad¯¹
To convert from a frequency f to angular velocity , simply multiply by 2:
Angular velocity and linear speed v are related by the equation:
Centripetal acceleration and force
Nothing will follow a circular path unless it is forced to.
Centripetal force is the force required to keep a body in uniform circular motion
Centripetal force and acceleration are always directed towards the centre of the circular path.