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Stitz-Zeager_College_Algebra_e-book

Y tan example 1034 1 suppose the terminal side of

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Unformatted text preview: ) or negative (in the case of clockwise motion), so that the quantity |v | quantiﬁes how fast the object s is moving - it is the speed of the object. Measuring θ in radians we have θ = r so that s = rθ and v= s rθ θ = =r· t t t The quantity θ is called the average angular velocity of the object. It is denoted by ω and t 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 time 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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