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Physics Dynamics Question

  1. Dec 4, 2008 #1
    1. The problem statement, all variables and given/known data

    Gear ‘B’ on the machine shown below accelerates from rest to 250 rpm in 2 seconds. Determine the angular velocity and acceleration of A, and the linear acceleration and velocity of rack C. See image attached



    2. Relevant equations

    I dunno where i would start off with this question, help would be appreciated.


    3. The attempt at a solution
     

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  3. Dec 4, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi tom23! Welcome to PF!:smile:

    (how far apart are the teeth on B compared with A and C? :confused:)

    First find the angular velocity and acceleration of B.

    Then you know that the "tooth-rates" on A B and C are the same … eg if B rotates through 7 teeth of the cog, then both A and C also move through 7 teeth. :wink:
     
  4. Dec 5, 2008 #3
    So I got this until now, is it right?

    ang velocity = 250 rpm x 2 pi x (1/60) = 26.2 rad/s

    ang acceleration = change in ang velocity / chang in time = 26.2 rad/s / 2s = 13.1 rad/s^2

    Thus at B: tangential Velocity at B = ang velocity*radius1 = 26.2*20 = 524 cm/s

    tangential Acceleration at B = ang acceler.*radius1 = 13.1*20 = 262 cm/s^2

    Therefore on A:

    Angul. Velocity at A = tang. velocity/radius2 = 524/15 = 34.9 rad/s
    Angul. Acceler at A = tang. acceler./radius2 = 262/15 = 17.5 rad/s

    Does this two answers sound right, now how would i go on to solve for linear accel. and velocity of rack C?
     
  5. Dec 5, 2008 #4

    tiny-tim

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    Yes, that's fine. :smile:
    You haven't answered my question: how far apart are the teeth on B compared with A and C?

    If they're the same distance apart, then your answer is right.
    Same method … you have the tangential velocity of A, so you can find the linear velocity of C.
     
  6. Dec 5, 2008 #5
    Tey didnt give the distance, so i believe it is the same, so for linear velocit and accel at C, i got:

    V = 34.9 (30cm) = 1047 cm/s
    a = 17.5 (30cm) = 525 cm/s

    Does it look right?

    Thanlks for all your help above!
     
  7. Dec 5, 2008 #6

    tiny-tim

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    Hi tom23! :smile:
    Yes … that's fine … if the teeth are all the same distance apart, then the tangential velocities and the linear velocity are all the same. :smile:

    (though I'd have done it directly from B … 26.2(40), rather than from A, as you did! :wink:)
     
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