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Rotational motion

  1. Dec 12, 2006 #1
    1. The problem statement, all variables and given/known data

    A wheel decellerates from 100 rpm in 10 sec. Find angular acceleration, torque and the force torque is producing on a fixed object.
    The wheel has a radius of .0025m and a mass of 50kg.

    2. Relevant equations
    T=Ia
    a=ra
    T=dL/dt


    3. The attempt at a solution

    The first thing I did was change rpm to rad/sec which gave me 10.5 rad/sec.
    for angular acceleration i used: a=ra-> .0025*10.5/10 which gave me
    a=.002625 rad/sec^2.
    For torque i used 1/2*50*.0025^2*1.05 which gave me .00016 kgm^2.
    I am not sure where to go with this now, or even if I am headed in the right direction. Any suggestions would be greatly appreciated.
     
  2. jcsd
  3. Dec 12, 2006 #2

    Hootenanny

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    You have not correctly found the angular acceleration. The definition of angular acceleration is;

    [tex]\alpha = \frac{d\omega}{dt}[/tex]
     
  4. Dec 12, 2006 #3
    wouldn't the dw in this case just be the 10.5 rad/sec divided by 10(then number of seconds it takes for the wheel to stop?
     
  5. Dec 12, 2006 #4

    Doc Al

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    I assume you mean:
    [tex]a = r \alpha[/tex]
    This relates angular acceleration to linear acceleration.
    OK.
    You are mixing up angular and linear acceleration. All you need is angular acceleration.
     
  6. Dec 12, 2006 #5
    yes, your formula for acceleration is the one i meant. I understand that dw/dt is angular acceleration, so do i just not multiply by the radius? I am very confused here.
     
  7. Dec 12, 2006 #6

    Doc Al

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    Correct. You would only multiply by the radius if you needed the linear acceleration (units: m/s^2) of a point on the rim of the wheel.
     
  8. Dec 12, 2006 #7
    ok so now that i know torque of the wheel is .00016kgm^2 and angular acceleration is 1.05 rad/sec^2. How do i figure out what the force is that the torque of the wheel is producing on a fixed object, say someone's head for example?
     
  9. Dec 12, 2006 #8

    Doc Al

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    If you assume that the torque is created by a force applied tangentially to the edge of the wheel, what force is required to generate that torque? (What's the definition of torque?)
     
  10. Dec 12, 2006 #9
    Torque = R xF or Torque = I alpha or Torque = dL/dt.
    I understand that these are the formulas for torque, I am just not sure which one I am supposed to use.
     
  11. Dec 12, 2006 #10
    I decided to try T=R x F. What I got was that the torque of the wheel is equal to the radius times the unknown F times the sin90.

    .00016=.0025F

    F=.064N
    Does this look right to you?
     
  12. Dec 12, 2006 #11

    Doc Al

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    Well, what are you trying to find? Which formula relates to that quantity?
     
  13. Dec 12, 2006 #12
    I am trying to find the force the torque exerts on the object The formula I used was Torque = R x F.
     
  14. Dec 12, 2006 #13

    Doc Al

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    Wise choice, since that's the only one that has force in it. :wink:

    Looks OK to me.
     
  15. Dec 12, 2006 #14
    Great thank you so much for all your help. :0)
     
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