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Rotational Motion and Moment of Inertia Questions

  1. Nov 14, 2005 #1


    A uniform rod of mass 0.93 kg is 17 m long.
    The rod is pivoted about a horizontal, fric-
    tionless pin at the end of a thin extension (of
    negligible mass) a distance 17 m from the cen-
    ter of mass of the rod. Initially the rod makes
    an angle of 70 degrees with the horizontal. The rod
    is released from rest at an angle of 70 degrees with
    the horizontal.
    The acceleration of gravity is 9.8 m/s^2.
    Hint: The moment of inertia of the rod
    about its center-of-mass is 1/12 ML^2.

    What is the angular speed of the rod at
    the instant the rod is in a horizontal position?
    Answer in units of rad/s.

    MgL/2 = .5(1/12ML^2)w^2

    This works out to be:

    w = sqrt(12g/L)

    w = 2.630142 ???

    But the answer is wrong?!?! why?!
    Two pulley wheels, or respective radii R1 =
    0.34 m and R2 = 1.5 m are mounted rigidly
    on a common axle and clamped together. The
    combined moment of inertia of the two wheels
    is I + 4.5 kg*m^2.
    Mass m1 = 18 kg is attached to a cord
    wrapped around the first wheel, and another
    mass m2 = 5.9 kg is attached to another cord
    wrapped around the second wheel.

    The acceleration of gravity is 9.8 m/s^2 :
    Find the angular acceleration of the system.
    Take clockwise direction as positive. Answer
    in units of rad/s^2.

    I = .5MR^2

    I1= .5(18)(.34)^2
    I2= .5(5.9)(1.5)^2

    I = I1 +I2 + 4.5 = 12.1779

    Acceleration= [(m2gR2)-(m1gR1)]/[I+(m1r1^2)+(m2r2^2)]

    = .971689752 ?!?!

    This is wrong as well, WHY!?!?!?

    Please help. All help is appreciated. :approve:
  2. jcsd
  3. Nov 14, 2005 #2
    someone pls help me!!!... any hints appreciated. :)
  4. Nov 14, 2005 #3


    User Avatar
    Homework Helper
    Gold Member

    How did you get that equation? Where have you used the fact that the rod is initially inclined at an angle of 70 degrees to the horizontal?
  5. Nov 14, 2005 #4
    What equation should I use then?

    I found a similar pbm online that used that equation- apparently it's wrong.
  6. Nov 14, 2005 #5


    User Avatar
    Homework Helper
    Gold Member

    Well, have you thought about what concept or principle you might use to attempt this question?
  7. Nov 14, 2005 #6
    I know it uses Moment of Inertia in the equation... that's abt it.

    I'm totally lost as to how to approach it.
  8. Nov 14, 2005 #7


    User Avatar
    Homework Helper
    Gold Member

    I understand that, but it's important to think in terms of principles and concepts rather than equations. The equations will easily follow once you understand what's happening.
    For instance,in this problem, what can you say about the energy of the system?
    Last edited: Nov 14, 2005
  9. Nov 14, 2005 #8
    Well, my brain isn't working at the moment.

    I'll look at this tomorrow. Thanks for your help, nandrie, vannakam _/\_ ;).
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