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Planar Kinematics of a Rigid Body

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data
    Due to an increase in power, the motor M rotates the shaft A with an angular acceleration(α=0.06θ^2) rad/s^2, where θ is in radians. If the shaft is initially turning at ω
    =50 rad/s, determine the angular velocity of gear B after the shaft undergoes an angular displacement Δθ=10 revolutions.

    2. Relevant equations
    ω^2=ωsub0^2+2α(θ-θsub0)
    v=ωr



    3. The attempt at a solution
    I converted 10 revs to 62.83 rad. I then used the first equation by subbing in ωsub0, α, and 62.83 for θ and θ-θsub0. I came up with 179.62rad/s for ωsubA. I then found the velocity of shaft A using v=ωr. vsubA=vsubB therefore I tried to find ωsubB using ω=v/r. This did not work. Any thoughts?
     
  2. jcsd
  3. Oct 3, 2011 #2

    gneill

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    Staff: Mentor

    What's the relationship between shaft A and gear B? Are there more gears? A picture would be nice.
     
  4. Oct 3, 2011 #3
    The driving shaft A has a radius of 12mm whereas gear B has a radius of 60mm. I don't have a picture but Shaft A is turning Gear B.
     
  5. Oct 3, 2011 #4

    gneill

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    Staff: Mentor

    Gear B is mounted co-axially on shaft A?
     
  6. Oct 3, 2011 #5
    The axis of both Shaft A and Gear B are parallel although not co-axial. Gear B is a spur gear driven by Shaft A.
     
  7. Oct 3, 2011 #6

    gneill

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    Staff: Mentor

    Seems to me that this information is important to the solution of the problem. We need to know the gearing ratio between shaft A and gear B in order to relate their angular motions.
     
  8. Oct 3, 2011 #7
    That information is not available. The only givens are: Drive shaft radius=12mm;Gear B radius=60mm;Drive shaft angular acceleration=0.06θ^2 rad/s^2; initial angular velocity of Drive shaft A= 50 rad/s. Find angular velocity of Gear B after 10revs of Drive shaft A.
     
  9. Oct 3, 2011 #8

    gneill

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    Staff: Mentor

    It looks like the acceleration isn't constant. It's of the form α = k*θ2, so finding the angular velocity of the shaft will require some calculus.
     
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