anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
linear velocity is how fast your going on the outer edge
amistre64
  • amistre64
we travel 2pi r, the circumference, in a given time span distance* time = speed
amistre64
  • amistre64
the 2 gears should be linearly the same

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More answers

amistre64
  • amistre64
2pi/20 = pi/10 parts of the circumference per second, right?
amistre64
  • amistre64
5*pi/10 = pi/2 per sec
amistre64
  • amistre64
that almost makes sense to me lol ...
amistre64
  • amistre64
2pi = 6. somehting so its moving quicker; i think i got my ration upside down
anonymous
  • anonymous
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?
amistre64
  • amistre64
i just cant recall the formulas so i gotta reinvent it :)
anonymous
  • anonymous
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.
amistre64
  • amistre64
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
amistre64
  • amistre64
20 is the angle in rads so I guess 20*5 = 100 rads per second
amistre64
  • amistre64
both gears are traveling at the same linear speed; or else one would always be catching up to the other
amistre64
  • amistre64
they differe in angular speeds simply becasue they rotate differently; but linearly they are equal
amistre64
  • amistre64
they cover equal distances in the same aount of time on their edges
anonymous
  • anonymous
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?
amistre64
  • amistre64
you ever see a small dog trying to keep up with a larger one?
amistre64
  • amistre64
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
anonymous
  • anonymous
That helps a lot!
amistre64
  • amistre64
:) insanity has its benefits lol
anonymous
  • anonymous
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..
amistre64
  • amistre64
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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