Pre-Calc Exam Notes 100

Pre-Calc Exam Notes 100 - used because straightening out...

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100 Chapter 4 Radian Measure §4.4 4.4 Circular Motion: Linear and Angular Speed distance s r θ time t = 0 time t > 0 Figure 4.4.1 Radian measure and arc length can be applied to the study of circular motion . In physics the average speed of an object is deFned as: average speed = distance traveled time elapsed So suppose that an object moves along a circle of radius r , traveling a distance s over a period of time t , as in ±igure 4.4.1. Then it makes sense to deFne the (average) linear speed ν of the object as: ν = s t (4.8) Let θ be the angle swept out by the object in that period of time. Then we deFne the (average) angular speed ω of the object as: ω = θ t (4.9) Angular speed gives the rate at which the central angle swept out by the object changes as the object moves around the circle, and it is thus measured in radians per unit time. Linear speed is measured in distance units per unit time (e.g. feet per second). The word linear is
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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.

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