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Calculating amount of revolutions

  1. Nov 17, 2010 #1
    1. The problem statement, all variables and given/known data
    A high-speed drill reaches 2760 rpm in 0.260 s. Through how many revolutions does the drill turn during this first 0.260 s?



    2. The attempt at a solution

    UPDATED:

    Here's what I have right now

    2760 rpm * (2n/1 rev) * (60 s / 1 min) = 1040495.49 rad/s

    1040495.49 rad/s * 0.260 s = 270,528.83 radians

    270,528.83 radians * (1 rev / 2n) = 43,056 revolutions

    Is that right? I haven't put the answer in because I have a limited amount of tries but I want to make sure I did it right.
     
    Last edited: Nov 17, 2010
  2. jcsd
  3. Nov 17, 2010 #2

    rock.freak667

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    when you converted rpm you got rad/s. So multiplying that by 0.26s will give you the radians it moved.

    now you know that 2π rad = 1 rev.

    You need to do another conversion to get the revolutions.
     
  4. Nov 17, 2010 #3
    I divided 11.96 by 2pi and got 1.90 revolutions, but the computer program says that's wrong. What's my mistake?
     
  5. Nov 17, 2010 #4
    You know the final (and initial) angular velocity and the time it took to get there. With this you can get the angular acceleration. Given that, you can find how many revolutions it traversed in the given time.
     
  6. Nov 17, 2010 #5

    rl.bhat

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    Hi smpolisetti, welcome to PF.
    in the problem. initial angular velocity is zero and final angular velocity = 2760*2π/60 rad./s.
    Find the angular acceleration using ω = ωο + α*t.
    Then find the angular displacement using θ = ωο*t + 1/2*α*t^2
     
  7. Nov 17, 2010 #6
    I know that the acceleration is 1110 rad/s/s but I don't know how to get the amount of revolutions from that
     
  8. Nov 17, 2010 #7

    rock.freak667

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    no no 2760 rpm you have.

    1 rpm = 2π/60 rad/s

    you do not need angular acceleration.

    Convert the rpm to rad/s and then multiply by the 0.26 sec.
     
  9. Nov 17, 2010 #8
    Here's what I have

    2760 rpm * (2n/1 rev) * (60 s / 1 min) = 1040495.49 rad/s

    1040495.49 rad/s * 0.260 s = 270,528.83 radians

    270,528.83 radians * (1 rev / 2n) = 43,056 revolutions

    Is that right? I haven't put the answer in because I have a limited amount of tries but I want to make sure I did it right.
     
  10. Nov 17, 2010 #9

    rl.bhat

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    Angular acceleration = 1100 rad/s/s.

    θ = ωο*t + 1/2*α*t^2

    θ = 1/2*1100*(0.26)^2

    find θ and then find n.
     
  11. Nov 17, 2010 #10
    Thanks so much!!
     
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