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Flywheel Rotation Question

  1. Feb 6, 2017 #1
    1. The problem statement, all variables and given/known data
    A flywheel turns through 40 rev as it slows from an angular speed of 1.5 rad/s to a stop.Assuming a constant acceleration,find the tme for it to come to rest.

    2. Relevant equations
    ##w-w_0=∝t##

    3. The attempt at a solution
    In Δt secon the change in w will be 1.5 and this time it will rotate 40 times..I tried every equaiton like
    0-1.5=∝t
    or
    40=1.5t-1/2∝t^2
    but I couldnt found
     
  2. jcsd
  3. Feb 6, 2017 #2
    There is another equation that you should know that involves initial and final velocities, acceleration and angle of rotation.
    Also, you are mixing units here: revolutions and radians.
     
  4. Feb 6, 2017 #3

    BvU

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    Check the units of your last equation (I wonder: why couldn't you solve it ? - or did it just give the wrong answer ?)
     
  5. Feb 6, 2017 #4
    I am really bad at this whole rotation-torque subject.I ll look again..I know my equation is wrong...
     
  6. Feb 6, 2017 #5

    ehild

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    What is the turning angle when the flywheel rotates 40 times?
    Also check the signs.
     
  7. Feb 6, 2017 #6
    turning angle ?
     
  8. Feb 6, 2017 #7

    ehild

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    Or angle of rotation. What is the angle the wheel rotates during one revolution?
     
  9. Feb 6, 2017 #8
    2π ?
     
  10. Feb 6, 2017 #9
    Are we turning 40 rev to 80π rad ??
     
  11. Feb 6, 2017 #10

    ehild

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    yes. And during 40 revolutions?
     
  12. Feb 6, 2017 #11
    I posted 80π ?
     
  13. Feb 6, 2017 #12

    ehild

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    Yes. So what are the equations for the change of angular velocity and angular rotation angle in time Δt?
     
  14. Feb 6, 2017 #13
    ##w-w_0=∝t##and
    ##Δθ=wt ##

    or ##Δθ=wt-\frac 1 2∝t^2##
     
  15. Feb 6, 2017 #14

    ehild

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    Δθ=wt is only valid for constant angular velocity.
    ##Δθ=w_0t+\frac {1 }{2}\alpha t^2## that is valid with positive sign.
    Eliminate alpha.
     
    Last edited: Feb 6, 2017
  16. Feb 6, 2017 #15
    I guess I have to study this more to understand the basics.I ll open another thread
     
  17. Feb 6, 2017 #16
  18. Feb 6, 2017 #17
    Δw=-1.5 and Δθ is 80 so

    Δw=-1.5=∝t and

    80=1.5t-1/21.5t

    Is this true ?
     
  19. Feb 6, 2017 #18
    The rotational equations pretty much follow directly from the linear equations. So if you can remember the linear equations, the rotational should be easy.
    v = vo + at → ω = ωo + αt
    v2 = vo2 + 2ax → ω2 = ωo2 + 2αθ
    x = vot + at2/2 → θ = ωot + αt2/2
    F = ma → Γ = Iα
    ρ = mv → L = Iω
    Ek = mv2/2 → Ek = Iω2/2

    I think so, except it should be 80π instead of 80.
     
  20. Feb 6, 2017 #19
    Ok,I found....Thanks all of you...Just couldnt see that
     
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