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Angular motion problem

  1. Jun 19, 2007 #1
    1. The problem statement, all variables and given/known data

    A wheel starts from rest and accelerates uniformly with an angular acceleration of 4rad/〖sec〗^2. What will be its angular velocity after 4 seconds and the total distance travelled in that time?


    2. Relevant equations



    3. The attempt at a solution

    i have got my answer and the unit is rad, i know that rad can be converted into degrees or even revs, but what about units in lengths (m)? or is the unit rad correct in my answer

    thanks
     
  2. jcsd
  3. Jun 19, 2007 #2

    malawi_glenn

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    You must know the radius of the weel.
     
  4. Jun 19, 2007 #3
    thanks, so if i have not got the radius of the wheel is my answer of 40rad correct?
     
  5. Jun 19, 2007 #4

    malawi_glenn

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    How did you get 40rad ?
     
  6. Jun 19, 2007 #5
    this is how i calculated the above:

    ω=0+4 rad/〖sec〗^2 x 4sec

    ω=0+16 rad/sec

    ω=16 rad/sec

    θ=1/2 (w_1+w_2 )t

    =1/2 (20 rad/sec)t

    =10 rad/sec x 4sec

    =40rad
     
  7. Jun 19, 2007 #6

    malawi_glenn

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    [tex] \omega = \omega _{0} + \alpha t [/tex]

    [tex]\theta = \theta _{0} + \omega _{0} t + \frac{1}{2} \alpha t^{2} [/tex]

    Now if alpha is constant 4
    and time t is 4, what do we get?
     
  8. Jun 19, 2007 #7
    ω=16 rad/sec (as shown in my answer)

    the 40rad is my total distance (does this need to be converted)?
     
  9. Jun 19, 2007 #8

    malawi_glenn

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    yes but the total angle covered is 32 rad

    theta = 0 + 0 + 0.5 * 4 * 4^2
     
  10. Jun 19, 2007 #9
    can you expain that a bit more as i dont know what you mean (sorry) so 40 rad is not the distance?
     
  11. Jun 19, 2007 #10

    malawi_glenn

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    [tex]\theta = \theta _{0} + \omega _{0} t + \frac{1}{2} \alpha t^{2} [/tex]

    This is the formula, right?

    The given values is alpha = 4 and time = 4. The initial angular veolcity is 0(starts from rest) and the theta_zero is also 0...
     
  12. Jun 19, 2007 #11
    [tex]\omega = \omega_{1} + \alpha t [/tex]

    this is the formula given in class (if it can be read)
     
  13. Jun 19, 2007 #12

    malawi_glenn

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    yes that gives you the new angular velocity, but you was also asking of the "lenght" covered by the weel in that time (4s)...

    The total "lenght", is given by the forumula i gave you in post #10, where omega_zero is the initial angular velocity (of course). Now what is the anser for theta?
     
  14. Jun 19, 2007 #13
  15. Jun 19, 2007 #14
    i have now worked out that angular velocity = 16rad/sec

    using [tex] \theta = {1/2} (\omega_{1} + omega_{2}) [/tex]

    i calculated the distance to be 32rad

    please confirm.
     
  16. Jun 19, 2007 #15

    malawi_glenn

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    yes that it correct, see my post #8 otherwise...
     
  17. Jun 19, 2007 #16
    thanks you have been a great help :)
     
  18. Jun 19, 2007 #17

    malawi_glenn

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