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Problem resolving forces into components

  1. Sep 22, 2014 #1
    I have problems with this question:

    62d306ea7ba4c5d56ff4ab351d23529e.png

    This is how I resolved v into its components (Vr and Vtheta):

    7b408312dc76a0833d3c8c657c5d2659.png

    So with this I get
    Vr = - V cos theta
    Vtheta = V sin theta

    However in my solution booklet the components are the other way around (Vr = - V sin theta, Vtheta = V cos theta) and I cannot figure out why. It makes no sense... am I right and the solution wrong?
     
  2. jcsd
  3. Sep 22, 2014 #2
    The solution manual is wrong.
     
  4. Sep 23, 2014 #3

    FactChecker

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    The extreme cases support you. When theta is small, (the piston is in line with the lever) almost all the change is in r and theta is almost constant. Conversely, when the lever arm is straight up (theta=90), r doesn't change and theta is the only thing changing. That puts the cos and sin where you have them.
     
  5. Sep 23, 2014 #4
    Thought so. Thanks. Another problem I have with the solution manual is that it says the magnitude of the total acceleration is zero and therefore the radial acceleration = angular acceleration (Ar = Atheta). Is this true? Because I thought the constant velocity only meant the tangential acceleration was zero... and there would be still be a normal acceleration equal to v^2 / r.
     
  6. Sep 23, 2014 #5
    Either the solution manual is wrong again, or you have misread it somehow. ##\ddot r## and ##\ddot theta## have different units, so they can't be equal unless 0.
     
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