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 n1 teeth and the second gear has n2 teeth. 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 ω1 and ω2 are the angular velocities of the first and second gears, respectively, then v2 = v1 r2ω2 = r1ω1 ω2 = r1 r2 ω1 ω2 = n1 n2 ω1. The first gear in a single-stage gear train has 44 teeth and an angular velocity of 4 revolutions per second. The second gear has 8 teeth. Find the angular velocity of the second gear. (Round your answer to two decimal places.) rad/sec
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
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 ω1 and ω2 are the angular velocities of the first and second gears, respectively, then
| v2 | = | v1 | ||
| r2ω2 | = | r1ω1 | ||
| ω2 | = |
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| ω2 | = |
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The first gear in a single-stage gear train has 44 teeth and an angular velocity of 4 revolutions per second. The second gear has 8 teeth. Find the angular velocity of the second gear. (Round your answer to two decimal places.)
rad/sec
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