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Force to stop a rotating object

  1. Mar 13, 2015 #1
    1. The problem statement, all variables and given/known data
    The 3.2kg , 37-cm-diameter disk in the figure is spinning at 350 rpm .

    How much friction force must the brake apply to the rim to bring the disk to a halt in 2.4s?

    2. Relevant equations
    F = m * a
    I = (1/2) * mass * radius2 (I probably need to use this but I can't figure out how it works in)
    rotational speed = rotations/sec * circumference

    3. The attempt at a solution
    I've tried going about it multiple ways, but I think I'm just leading myself in circles

    Going to try to solve using F = m * a

    Solving for a:
    350 rpm / 60 seconds = 5.83 rotations/second
    5.83 rotations / second * (2π * .37m / 2) m/rotation = 6.77 m/s

    If I want to go from that to 0 m/s in 2.4s then it's (6.77m/s) / 2.4s = 2.82 m/s2

    So since F = m * a = 3.2kg * 2.82 m/s2 = 9.03 N

    Except that answer is wrong.

    I would love to use the different rotational formulas but I can't figure out what I'm supposed to use and when to switch from radians to meters and such.
     
  2. jcsd
  3. Mar 13, 2015 #2
    Also tried this:

    Net torque = I * α
    I = (.5 * 3.2kg * .185m2) = .0548 kg*m2
    α = ((350rpm / 60 s) - 0) * 2π / 2.4s = 15.27 rad/s

    Net torque = .0548 * 15.27 = .8363 Nm

    Net torque = F * radius
    .8363 = F * .185

    F = 4.52 N

    This one seems more correct but I've done it wrong so many times I don't know if I'm losing my mind.

    Edit: Also this one is exactly 1/2 my other answer so I assume in the other one or in this one I divided/multiplied by 2 somewhere when I shouldn't have.
     
  4. Mar 13, 2015 #3

    CWatters

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    #2 is on the right track.

    Force = mass * acceleration ..... is the linear case
    Torque = Moment of inertia * angular acceleration ...... is the same thing but for rotation.

    You didn't post a diagram but I assume it's a disc so I = 0.5*m*r2

    Where do you get 0.185m2 ?

    That should be rad/s2 because α is the angular acceleration.
     
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