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How many revolutions did the fish make?

  1. Jun 26, 2016 #1
    1. The problem statement, all variables and given/known data
    A fish starts at rest and uniformly accelerates. After 10 seconds, he is swimming around a rock at a rate of 3.14 rad/sec.
    a.) What's the magnitude of angular acceleration?
    b.) How many times did the fish circle the rock (how many revolutions?)

    2. Relevant equations
    a.) wf=wi+alpha*t

    3. The attempt at a solution
    a.)wf=wi+alpha*t
    alpha=(wf-wi)/t
    alpha=(3.14rad/sec-0)/10sec
    therefore, angular accelerate = .314 rad/sec^2

    b.) .314rad/sec^2 *1rev/2pi rad = 0.50 revolutions around the rock.

    I just wanted to double check that i did part b correctly because i guess i'm having trouble seeing how the sec^2 on the bottom of the units end up disappearing to become just revolutions.
     
  2. jcsd
  3. Jun 26, 2016 #2

    mfb

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    Staff: Mentor

    Where does that calculation come from? It is wrong. As you noted, the units don't match - and you did not use the time here, which is another sign that something is wrong.
     
  4. Jun 26, 2016 #3
    well all i did was use the conversion to convert rad to rev, i didn't use any type of formula, so perhaps i shouldnt be using the angular acceleration in part b?
    should i just take the 3.14 rad/sec and multiply it by the 10 secs to get 31.4 rad and then divide by 2pi to get around 5.00 revolutions?
     
  5. Jun 26, 2016 #4

    mfb

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    No, that would assume a constant angular velocity.


    If you start at rest on a street with a constant linear acceleration of 4 m/s2, how far do you go within 10 seconds?
    For rotations the situation is nearly the same.
     
  6. Jun 26, 2016 #5
    oh okay, i see that i need to include the angular acceleration.

    so i found this formula, 1/2*alpha*time^2
    (.314 rad/sec^2)*(100 sec^2)*(.5)=15.7 rad *1rev/2pi rad = 2.50 revolutions
     
  7. Jun 26, 2016 #6

    mfb

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    Right.
     
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