Angular velocity of three gears attached (showed work)

1. Sep 26, 2010

howru

1. The problem statement, all variables and given/known data[/b]
The operation of “reverse” for a three-speed automotive transmission is illustrated schematically in the figure.
If the shaft is turning with an angular velocity of Wg= 30 rad/s, determine the angular velocity of the drive shaft H. Each of the gears rotates about a fixed axis. Note that gears A and B , C and D , E and F are in mesh. The radius of each of these gears is reported in the figure.

2. Relevant equations
velocity=w * r (w is angular velocity)
"C:\Users\apoorva\Pictures\gears.jpg"[/URL]

[b]3. The attempt at a solution[/b]

So the angular velocity of shaft G is 30 rad/s.
I know that the velocity of B and A are same.
V[SUB]g[/SUB]=30(0.09)=2.7 m/s=V[SUB]a[/SUB]
W[SUB]a[/SUB]R[SUB]a[/SUB]=W[SUB]b[/SUB]R[SUB]b[/SUB]

angular velocity of W[SUB]b [/SUB]and W[SUB]c[/SUB] is the same--> 90 rad/s

V[SUB]c[/SUB]=V[SUB]d [/SUB]so W[SUB]c[/SUB]R[SUB]c[/SUB]=W[SUB]d[/SUB]R[SUB]d[/SUB]
90(.3)=W[SUB]d[/SUB](.05)

W[SUB]d[/SUB]R[SUB]d[/SUB]=W[SUB]e[/SUB]R[SUB]e[/SUB]
54(.05)=W[SUB]e[/SUB](.07)

W[SUB]e[/SUB]R[SUB]e[/SUB]=W[SUB]f[/SUB]R[SUB]f[/SUB]
38.6(.07)=W[SUB]f[/SUB](.06)

But I keep getting the answer wrong and I don't know what I am doing.

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2. Sep 26, 2010

MHrtz

Where's the diagram?

3. Sep 27, 2010

howru

i don't the link is working, but I posted an attachment which is at the end of the post called "gears"

4. Sep 27, 2010

howru

5. Sep 27, 2010

MHrtz

How did you multiply 30 and .5 and get 2.7?

6. Sep 27, 2010

howru

I meant 30*(.09)=2.7
not 0.05. sorry about that. I changed it in my post.
Because r=0.09 m is the radius of gear A

7. Sep 27, 2010

MHrtz

I think I can help you out. I think you need to use gear ratios.

The speeds of gears can be determined by their gear ratio

If a particular gear moves at say 30 rad/s and has a radius of 4 and that same gear moves another with a radius of 6 than you can find the speed of the second gear by using a ratio

In this case the gear ratio would be 1.5:1. This means that whenever the first gear rotates 1 and half times the second gear rotates only once.

8. Sep 27, 2010

howru

how did you get 1.5:1. is from using your numbers or the radius from my problem?

Ok, looking from my problem

Shaft G is 30 rad/s and gear A has the same angular velocity because the shaft is connected to gear A. Radius of gear A is 0.09 meters.

The second gear is B and it's radius is 0.03.
Gear ratio=0.09:0.03 which is 3:1, right?
then I would use that to find my velocity?
So speed of Gear B is=30(3)-->90 rad/s.

Then Gear B and Gear C are the same because the radius is the same.

So Gear C has 90 rad/s which has a radius of 0.03m.
Gear D has 0.05m.
Gear ratio=0.05:0.03--> 1.67:1
then speed of Gear D is (1.67m)(90)=150
..etc.
right. that's the idea?

I understand what you are saying and I'm going to do that. but I'm a little confused about the ratios.

how do you simplify ratios with decimals: so from above .05:.03, would it 1.67:1
OR since .05/.03 is 5/3, would it 3:5

9. Sep 27, 2010

howru

never mind you got 1.5 by 6/4.

I got it. just ignore my ratios questions.

10. Sep 27, 2010

MHrtz

Well if 90mm is 3 times as big as 30mm than that is a ratio of 3:1. Likewise if a gear is .05m and the other is .03m than it is a 5:3 ratio. a 5:3 ratio is the same as a 1.67:1 ratio mathematically.

11. Sep 27, 2010

MHrtz

What book are you using? Are using Engineering Mechanics: Dynamics (12th edition) by Hibbeler because if you are then Wg is incorrect. it should be 60rad/s not 30rad/s.

12. Sep 28, 2010

howru

i'm using the 11th edition but my homework is on masteringengineering.com so sometimes the website changes the numbers.