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Homework Help: Tangential and centripetal acceleration problem

  1. Nov 1, 2009 #1
    A windmill starts from rest and rotates with a constant angular acceleration of 0.25 rad/s2. How many seconds after starting will the magnitude of the tangential acceleration of the tip of a blade equal the magnitude of the centripetal acceleration at the same point?

    I dont exactly know where to start with this problem. Wouldnt I need the radius to solve for the tangential acceleration as well as the centripetal acceleration?
  2. jcsd
  3. Nov 1, 2009 #2


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    It might work out without r. Give it a try! I suggest you begin with putting that condition into symbols:
    tangential acceleration = centripetal acceleration
    rα = v²/r (pardon the poor alpha character after the first r)
    Fill in the details and see if the r's cancel out!
  4. Nov 1, 2009 #3

    Andrew Mason

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    No. You have to work it out to see why.

    What is the tangential acceleration (convert angular acceleration to tangential acceleration - use r for the radius).

    Now, write out the expression for centripetal acceleration of a mass located at the tip in terms of angular speed.

    At what speed does the centripetal acceleration equal the tangential acceleration?

  5. Nov 2, 2009 #4
    I dont see how the r's can cancel out with ra = v^2/r

    And how can I covert angular acceleration to tangential acceleration?
  6. Nov 2, 2009 #5


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    It was rα = v²/r where the 2nd character is an alpha, angular acceleration.
    No r's cancel at this point, but you are given that α = .25 and of course v = rω.
    Since it is constant angular acceleration, you can also get a value for ω as a function of time . . . just keep working on that equation with these details and see what happens.
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