Pre-Calc Exam Notes 102

Pre-Calc Exam Notes 102 - 102 Chapter 4 Radian Measure 4.4...

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102 Chapter 4 Radian Measure §4.4 Example 4.17 A gear with an outer radius of r 1 = 5 cm moves in the clockwise direction, causing an interlocking gear with an outer radius of r 2 = 4 cm to move in the counterclockwise direction at an angular speed of ω 2 = 25 rpm. What is the angular speed ω 1 of the larger gear? r 1 = 5 cm r 2 = 4 cm ω 2 = 25 rpm Figure 4.4.2 Solution: Imagine a particle on the outer radius of each gear. After the gears have rotated for a period of time t > 0, the cir- cular displacement of each particle will be the same. In other words, s 1 = s 2 , where s 1 and s 2 are the distances traveled by the particles on the gears with radii r 1 and r 2 , respectively. But s 1 = ν 1 t and s 2 = ν 2 t , where ν 1 and ν 2 are the linear speeds of the gears with radii r 1 and r 2 , respectively. Thus, ν 1 t = ν 2 t ν 1 = ν 2 , so by formula (4.10) we get the fundamental relation between the two gears: ω 1 r 1 = ω 2 r 2 (4.11) Note that this holds for any two gears. So in our case, we have
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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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