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Angular Velocity Calculation

  1. Jun 19, 2016 #1
    1. The problem statement, all variables and given/known data
    6yXk1RF.png

    2. Relevant equations
    v = w x r

    3. The attempt at a solution
    I got the answer correct after a few tries, but I am little confused on why it has to solved this specific way. I know that v = w x r, so why can I not just say w = v/r? Is it because w is measured from the center of the roller so v = w x r would be vcenter, not vtop?
    That is how I ended up solving it, but I wanted to make sure I didn't get there "accidentally" or misinterpreted the process.
    eCy96Ra.png
    Using that diagram and concept of similar triangles:
    tan θtop = tan θcenter
    Stop/2r = Scenter/r
    Stop = 2*Scenter, Scenter = rθ
    Stop = 2rθ
    d(Stop)/dt = vtop = d(2rθ)/dt = 2rθ' = 2rωtop
    thus, ω = v/2r

    Any reasoning as to why I have to do this would be much appreciated!!
     
  2. jcsd
  3. Jun 19, 2016 #2
    That's for the centro of the motion is at the bottom of the roller. Your formula should be applied as ##v=2r\cdot\omega,## where ##2r## is the distance from the bottom to the top.
     
  4. Jun 20, 2016 #3
    Ahh, i forgot, when using v = w x r you have to always measure from from IC unless using relative velocity equation. Thank you!
     
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