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Unformatted text preview: used because straightening out the arc traveled by the object along the circle results in a line of the same length, so that the usual deFnition of speed as distance over time can be used. We will usually omit the word average when discussing linear and angular speed here. 4 Since the length s of the arc cut off by a central angle in a circle of radius r is s = r , we see that = s t = r t = t r , so that we get the following relation between linear and angular speed: = r (4.10) 4 Many trigonometry texts assume uniform motion, i.e. constant speeds. We do not make that assumption. Also, many texts use the word velocity instead of speed. Technically they are not the same; velocity has a direction and a magnitude, whereas speed is just a magnitude....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Arc Length

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