# Speed of shaft connected to gear

1. Jul 18, 2011

### vidhyarthi

Hi all,
I'm an EE student and i have least knowledge about working of gears.
I just want to know that if there are two shafts S1 and S2 of same diameter having two gears G1 and G2 mounted on them respectively. The gear ratio is 1:2. And the shaft S1 is connected to a motor which rotates at 1000rpm. Then
Will the shafts S1 and S2 rotate at same rpm. If yes then why people say that gears are used to increase or decrease speeds. If no how their speeds are differed?

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Last edited: Jul 18, 2011
2. Jul 18, 2011

### edgepflow

Keep these two things in mind about gears:

a) The tangential velocity is the same for both gears.
b) The number of teeth is proportional to the diameter of the gear.

As a consequence of a)

v = contant = R1 X angular speed 1 = R2 X angular speed 2

As a consequence of b)

gear ratio = ratio of teeth = ratio of diameters

So for a gear ratio of 2:1, the rpm ratio is also 2:1.

3. Jul 18, 2011

### xxChrisxx

You need to be really careful how you write the gear ratios down, as what you've put doesn't match the drawing.

It's:
Input teeth:Output teeth

Gears can be visualised as two circles touching at a single point. With the respective diamaters being the ratio of the gears.

So you say the ratio is 2:1, but the picture shows a 1:2 ratio as the output gear is larger.

4. Jul 18, 2011

### vidhyarthi

But actually rpm is inversely proportional to diameter of the rotating object then if gear ratio i.e. the ratio of diameters is 2:1 then i think the rpm is 1:2. Is it true?

Sorry i thought that gear ratio as the ratio of their speeds.

And what happens to the shaft rotation will they rotate at equal rpm?

5. Jul 18, 2011

### xxChrisxx

The shafts rotate at the same speed as their respective gears.

6. Jul 18, 2011

### vidhyarthi

Final question(i think i can understand fully with this)
Let the diameter of shaft S1=S2=19mm and S1 is a motor shaft rotating at 3000rpm.
from rpm=(kmphx1000)/(60xA) the speed of shaft is 10.744kmph
The gear G1 with diameter 150mm rotates at 380rpm and the gear G2 rotates at 190rpm(got from above formula)
then at what rpm the shaft S2 rotates 3000 or 190??

7. Jul 18, 2011

### xxChrisxx

Why are you saying the gears are rotating at different speeds to the shafts? Also where on earth did you find that formula?

8. Jul 18, 2011

### vidhyarthi

I'm saying that because gear has more diameter than shaft and from your question can i understand that shaft just deliver power to any thing connected to it i.e same torque and same speed.
And coming to the formula i got it here http://wiki.answers.com/Q/What_is_the_formula_for_converting_rpm_to_kph