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or negative (in the case of clockwise motion), so that the quantity |v | quantiﬁes how fast the object
is moving - it is the speed of the object. Measuring θ in radians we have θ = r so that s = rθ and v= s
t The quantity θ is called the average angular velocity of the object. It is denoted by ω and
read as ‘omega-bar’. The quantity ω is the average rate of change of the angle θ with respect to
time and thus has units radians . If ω is constant throughout the duration of the motion, then it
can be shown17 that the average velocities involved, v and ω are the same as their instantaneous
counterparts, v and ω , respectively. That is, v , simply called the ‘velocity’ of the object, is the
instantaneous rate of change of the position of the object with respect to time.18 Similarly, ω is
called the ‘angular velocity’ and is the instantaneous rate of change of the angle with respect to
time. If the path of the object were ‘uncurled’ from a circle...
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