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Radial force on a particle with circular motion

  1. Oct 16, 2012 #1
    A particle of mass 0.014 kg is travelling on a radius 0.9m at a rotational velocity of 36+5*t rad.s-1.


    How many revolutions does the particle go thorugh in 4.8 seconds? [revs]


    What is the radial force on the particle at 4.8 seconds? [N] (Hint: consider directions)
    (question i'm stuck on)


    What is the absolute magnitude of force on the particle at 4.8 seconds? [N]



    We know that the radial acceleration = v^2/r



    To find the amount of revolutions I simply integrated the rotational velocity with respect to time, and found that the particle rotated 230.4 radians or 36.69 revs.

    The second question is the question that I seem to be getting wrong. The way I tried to solve it was by firstly finding the rotational velocity after 4.8 seconds:
    w = 36+5*4.8
    = 60 rad/s

    thus we know that the translational velocity is:
    v= rw
    = 60*0.9
    = 54 m/s

    we know that the radial acceleration, ra, can be defined by:
    ra = v^2/r
    = 54^2/0.9
    = 3240

    thus the radial force, Fr, is:
    Fr = m*ra
    =0.014*3240
    =45.36 N

    the above question i am getting wrong for some reason. any help would be appreciated




    For the final question we know that the angular acceleration is 5 rad/s^2
    this means the linear acceleration of the particle is 4.5 m/s.

    we know the translational force will be Ft=m*a
    Ft = 0.014*4.5
    = 0.063

    So we can work out the total magnitude of the force like so:
    F_tot = sqrt(0.063^2+45.36^2)
    = 45.36
     
  2. jcsd
  3. Oct 16, 2012 #2

    BruceW

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    Homework Helper

    hi lee, welcome to physicsforums :)
    Your answer looks good to me. Maybe they also wanted the direction of the radial force at that time.
     
  4. Oct 16, 2012 #3
    Thanks for answering, I think its got something to do with the consider directions hint, but im not sure what I've done wrong. I don't think they want the direction of the radial force because they didn't give a starting position for the particle, so we don't know the direction of the force.
     
  5. Oct 17, 2012 #4

    BruceW

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    Homework Helper

    ah, that's true, they don't give the starting position. Then maybe you are meant to give the direction of the radial force, compared to its direction at t=0 ? This is a bit of a stretch, but I can't imagine what else they want for the answer...
     
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