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A pulley with rotational inertia

  1. Dec 3, 2009 #1
    1. The problem statement, all variables and given/known data

    A pulley, with a rotational inertia of 2.0 10-3 kg·m2 about its axle and a radius of 20 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t2, where F is in newtons and t in seconds. The pulley is initially at rest.

    (a) At t = 4.0 s what is its rotational acceleration?
    1 rad/s2
    (b) At t = 4.0 s what is its rotational speed?
    2 rad/s


    2. Relevant equations

    Torque = I * alpha

    Torque = |r||F|sin(theta)


    3. The attempt at a solution

    I have only tried part a. What I did was since I know the radius = .020 m, F, and I, I rearranged the formulas like so:

    alpha = Torque / I

    Since it's tangent, sin(90) = 1 therefore Torque = r*F

    F at 4s = 6.8 N and multiplying this by the radius .020 m gives a torque of .136 Nm

    So now alpha = .136 Nm / .002 kgm^2 = 68 rad/s^2

    I plugged that in on webassign and it was wrong so apparently I'm not doing something right. Any guidance is appreciated, thanks.
     
  2. jcsd
  3. Dec 3, 2009 #2

    kuruman

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    Your method for calculating the angular acceleration is correct. However 20 cm = 0.20 m not 0.02 m.
     
  4. Dec 3, 2009 #3
    Yep, I had a friend tell me I converted incorrectly. Thanks :)

    From there though, my alpha = 680 rad /s^2

    The equation for rotational veloctiy is:

    omega(t) = omega (initial) + alpha (t)

    so with alpha = 680 rad/s^2 and t = 4s that should give me a rotational speed of 2720 rad/s

    This, however, is incorrect as well. The initial omega = 0 rad/s because the pulley is initially at rest. What am I doing wrong here??
     
  5. Dec 3, 2009 #4

    ideasrule

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    The equation omega(t) = omega (initial) + alpha (t) only works for constant angular acceleration. Here, force is F = 0.50t + 0.30t2, so alpha can't possibly be constant. You'll have to use integration to get the speed.
     
  6. Dec 3, 2009 #5
    Thanks :) I integrated from 0 to 4 of F(t) and got 10.4. using the constants I and R, I was able to get the correct answer. Thanks again.
     
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