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?

Question

amistre64 · Answer

linear velocity is how fast your going on the outer edge

amistre64 · Answer

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

amistre64 · Answer

the 2 gears should be linearly the same

amistre64 · Answer

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

amistre64 · Answer

5*pi/10 = pi/2 per sec

amistre64 · Answer

that almost makes sense to me lol ...

amistre64 · Answer

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

anonymous · Answer

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 · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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 · Answer

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

amistre64 · Answer

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 · Answer

That helps a lot!

amistre64 · Answer

:)  insanity has its benefits lol

anonymous · Answer

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 · Answer

yes, same linear velocity; the smaller wheel just has to turn around quicker to cover the same distance so its angle speed is faster