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Determine the angular velocity and angular displacement

  1. Apr 27, 2009 #1
    1. The problem statement, all variables and given/known data
    The pinion gear A has a constant angular acceleration of 3 rad/s^2. Determine the angular velocity and angular displacement of the output shaft C @ t=2s starting from rest. The shaft is fixed to B and turns w/ it.

    A has a radius of 35mm, B has a radius of 125mm, C is unkhown radius



    2. Relevant equations

    just a note. when i use a = angular acceleration



    3. The attempt at a solution

    First I found the angular velocity at A
    w(a) = w(0) + at where w(0) = 0, a = 3rad/s^2, t=2
    =6rad/s
    Next I transfered it to the bigger gear B
    w(a)r(a) = w(b)r(b) where w(a) = 6rad/s, r(a) = 35mm, r(b) = 125mm
    there fore w(b) = 1.68 ras/s
    a(a)r(a) = a(b)r(b) where a(a) = 3rad/s^2, r(a) = 35mm, r(b) = 125mm
    therefore a(b) = .84 ras/s^2

    Since B & C are conected is a(b) = a(c).

    I then tried to find the angular displacement @ c

    a d(pheta) = w dw which gives .84pheta = .5w(b)^2
    pheta = 1.68 rad.

    But 1.68 rad is the angular velocity at B. Is this correct
     

    Attached Files:

  2. jcsd
  3. Apr 27, 2009 #2

    LowlyPion

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    Homework Helper

    Re: Rotation

    Looks to me like they are both 1.68 .

    ω = a*t

    θ = 1/2 a*t2 or

    2*θ = a*t*t

    But when t = 2 that means

    θ = 2*a = ω
     
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