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Two problems involving rotational movement

  1. Oct 31, 2007 #1
    1. First Problem

    1. The problem statement, all variables and given/known data
    A disc with mass of 50kg and radius of 20cm is rotating with a frequency of 480rpm, and after 50 seconds, as a result of the force of friction, it stops. What's the moment (momentum of force, torque) if during the rotation the disc made 200 rotations?


    2. Relevant equations
    [tex]M=I\epsilon[/tex]


    3. The attempt at a solution
    [tex]R=0,2m; m=50kg; f=480min^{-1}=8Hz; t=50s; N=200;[/tex]
    [tex]w_0=\frac{2\pi}{1/8}=16\pi rad/s[/tex]
    [tex]w = 0rad/s[/tex]
    [tex]\epsilon=\frac{w-w_o}{t}=\frac{-16\pi}{50}rad/s[/tex]
    [tex]I=0.5mR^2=1[/tex]

    [tex]M=I\epsilon=-1.21924Nm[/tex]

    Is this correct? I can't see where to number of total rotations (angular distance) fits in, or maybe it's a distractor?

    2. Second problem

    1. The problem statement, all variables and given/known data
    А rope is wrapped around a horizontal cylinder with [tex]M=17kg; R=0,1m[/tex]. A bob with [tex]m=5kg[/tex] is attached at the end of the rope, at height of [tex]h=4m[/tex] above ground. The momentum of inertia of the cylinder is calculated with [tex]I=\frac{MR^2}{2}[/tex].

    a) what's the speed of the bob when it hits ground?
    b) calculate the total energy of the system.

    2. Relevant equations

    3. The attempt at a solution
    I've solved b) pretty easily,
    [tex]E=mgh=192,2J[/tex] which conforms to the solution in the book (so, the potential energy of the cylinder is ignored).

    I've tried solving a) this way
    [tex]mgh=\frac{mv^2}{2}+\frac{I\omega^2}{2}[/tex]
    If the liner velocity of the cylinder is equal to the speed of the bob at any given time, then we can substitute [tex]\omega=\frac{v}{R}[/tex]
    [tex]\vdots[/tex]
    Is this approach correct? I don't get the same solution with the one given in the book.
     
    Last edited: Nov 1, 2007
  2. jcsd
  3. Nov 1, 2007 #2


    Problem 1 seems fine.

    Kinetic energy of the cylinder should be [tex]\frac{I\omega^2}{2}[/tex] and not [tex]\frac{M\omega^2}{2}[/tex], ain't it?
     
  4. Nov 1, 2007 #3
    Yes, it was a mistype :)
     
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