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1. Find the angular velocity of the second gear. (Ro

1. Find the angular velocity of the second gear. (Ro

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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The following figure shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n, teeth and the second gear has n2 teeth. Gear 1 Gear 2 (n1, @) (n2, 02) Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If w, and w, are the angular velocities of the first and second gears, respectively, then V2 = V1 rzw2 = r1W1 W2 = n2 The first gear in a single-stage gear train has 43 teeth and an angular velocity of 2 revolutions per second. The second gear has 10 teeth. Find the angular velocity of the second gear. (Round your answer to two decimal places.) 9 X rad/sec Need Help? Read It Watch It
Transcribed Image Text:The following figure shows a single-stage gear train. Gear trains are used in many products, such as clocks and automotive transmissions, to reduce or increase the angular velocity of a component. The size of each gear is measured by the number of teeth rather than the radius. Suppose the first gear has n, teeth and the second gear has n2 teeth. Gear 1 Gear 2 (n1, @) (n2, 02) Because the spacing of the teeth is the same for both gears, the ratio of their radii will be equivalent to the corresponding ratio of the number of teeth. When two gears are meshed together, they share the same linear velocity. If w, and w, are the angular velocities of the first and second gears, respectively, then V2 = V1 rzw2 = r1W1 W2 = n2 The first gear in a single-stage gear train has 43 teeth and an angular velocity of 2 revolutions per second. The second gear has 10 teeth. Find the angular velocity of the second gear. (Round your answer to two decimal places.) 9 X rad/sec Need Help? Read It Watch It
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