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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- amistre64

linear velocity is how fast your going on the outer edge

- amistre64

we travel 2pi r, the circumference, in a given time span
distance* time = speed

- amistre64

the 2 gears should be linearly the same

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- amistre64

2pi/20 = pi/10 parts of the circumference per second, right?

- amistre64

5*pi/10 = pi/2 per sec

- amistre64

that almost makes sense to me lol ...

- amistre64

2pi = 6. somehting so its moving quicker; i think i got my ration upside down

- 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

i just cant recall the formulas so i gotta reinvent it :)

- 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

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

20 is the angle in rads so I guess 20*5 = 100 rads per second

- amistre64

both gears are traveling at the same linear speed; or else one would always be catching up to the other

- amistre64

they differe in angular speeds simply becasue they rotate differently; but linearly they are equal

- amistre64

they cover equal distances in the same aount of time on their edges

- 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

you ever see a small dog trying to keep up with a larger one?

- 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

That helps a lot!

- amistre64

:) insanity has its benefits lol

- 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

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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