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anonymous

  • 4 years ago

Angular and Linear Velocity... A small gear of radius 5 cm is turning with an angular velocity of 20 radians per second. It drives a large gear of radius 15 cm. What is the linear velocity of the teeth on the large gear?

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  1. amistre64
    • 4 years ago
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    linear velocity is how fast your going on the outer edge

  2. amistre64
    • 4 years ago
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    we travel 2pi r, the circumference, in a given time span distance* time = speed

  3. amistre64
    • 4 years ago
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    the 2 gears should be linearly the same

  4. amistre64
    • 4 years ago
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    2pi/20 = pi/10 parts of the circumference per second, right?

  5. amistre64
    • 4 years ago
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    5*pi/10 = pi/2 per sec

  6. amistre64
    • 4 years ago
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    that almost makes sense to me lol ...

  7. amistre64
    • 4 years ago
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    2pi = 6. somehting so its moving quicker; i think i got my ration upside down

  8. anonymous
    • 4 years ago
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    I got a linear velocity for the large gear of 300 cm per second when I used the equation using angular velocity of the small gear... I think I'm doing it correctly but I'm really not sure?

  9. amistre64
    • 4 years ago
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    i just cant recall the formulas so i gotta reinvent it :)

  10. anonymous
    • 4 years ago
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    The formula given says v=w(r), v being the linear velocity, w being angular, and r being the radius. Trig is kicking my butt.

  11. amistre64
    • 4 years ago
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    6.3662 pi per second 2pi * n = 6.3662 pi n = 6.3662/2 = 3.1631 or thereabouts yeah; radius * angle swept out = distance travled

  12. amistre64
    • 4 years ago
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    20 is the angle in rads so I guess 20*5 = 100 rads per second

  13. amistre64
    • 4 years ago
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    both gears are traveling at the same linear speed; or else one would always be catching up to the other

  14. amistre64
    • 4 years ago
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    they differe in angular speeds simply becasue they rotate differently; but linearly they are equal

  15. amistre64
    • 4 years ago
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    they cover equal distances in the same aount of time on their edges

  16. anonymous
    • 4 years ago
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    Okay okay that makes a lot more sense now. But the angular speed changes because the distance the gear covers is different for different sizes? Is that correct?

  17. amistre64
    • 4 years ago
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    you ever see a small dog trying to keep up with a larger one?

  18. amistre64
    • 4 years ago
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    if they cover the same distance in the same amount of time they are linearly equal; but the smaller one has to move alot faster becasue of its size; they are angularly different

  19. anonymous
    • 4 years ago
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    That helps a lot!

  20. amistre64
    • 4 years ago
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    :) insanity has its benefits lol

  21. anonymous
    • 4 years ago
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    So would a drive and wheel sprocket and wheel work the same way? They are connected by a chain, so they would all have the same linear velocity as well..

  22. amistre64
    • 4 years ago
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    yes, same linear velocity; the smaller wheel just has to turn around quicker to cover the same distance so its angle speed is faster

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