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Homework Help: Angular velocity of three gears attached (showed work)

  1. Sep 26, 2010 #1
    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]
    2.7/0.03=90 rad/s =Wb

    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]=54 rad/s

    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]=38.6 rad/s

    W[SUB]e[/SUB]R[SUB]e[/SUB]=W[SUB]f[/SUB]R[SUB]f[/SUB]
    38.6(.07)=W[SUB]f[/SUB](.06)
    W[SUB]f[/SUB]=45.03 rad/s

    Therefore W[SUB]h[/SUB]=45.03 rad/s

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

    Attached Files:

    Last edited by a moderator: Apr 25, 2017
  2. jcsd
  3. Sep 26, 2010 #2
    Where's the diagram?
     
  4. Sep 27, 2010 #3
    i don't the link is working, but I posted an attachment which is at the end of the post called "gears"
     
  5. Sep 27, 2010 #4
    anyone, please help!!!!
     
  6. Sep 27, 2010 #5
    How did you multiply 30 and .5 and get 2.7?
     
  7. Sep 27, 2010 #6
    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
     
  8. Sep 27, 2010 #7
    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

    Gear ratio = Radius of larger gear/radius of smaller gear

    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.
     
  9. Sep 27, 2010 #8
    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
     
  10. Sep 27, 2010 #9
    never mind you got 1.5 by 6/4.

    I got it. just ignore my ratios questions.
    thanks for your help.
     
  11. Sep 27, 2010 #10
    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.
     
  12. Sep 27, 2010 #11
    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.
     
  13. Sep 28, 2010 #12
    i'm using the 11th edition but my homework is on masteringengineering.com so sometimes the website changes the numbers.
     
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