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Finding COM, and inertia please help my answers don't make sense?

  1. Apr 20, 2012 #1
    Finding COM, and inertia please help my answers don't make sense??

    1. The problem statement, all variables and given/known data

    Find the center of mass of the object shown in the figure below?

    LINK TO FIGURE:
    http://s1168.photobucket.com/albums/r497/amy_parker1/?action=view&current=Untitled.jpg

    1. Find the center of mass of the object shown in the figure below.

    2. Calculate the rotational inertia of the object about the x-axis.

    3. From this value, deduce the rotational inertia of the object about an axis parallel to the x-axis, and going through the center of mass.

    m1=2.5kg , m2=5kg, m3=2.5kg , m4=5kg

    2. Relevant equations

    COM

    Inertia?

    3. The attempt at a solution

    my answers don't make sense

    for COM I got 2
     
  2. jcsd
  3. Apr 20, 2012 #2

    NascentOxygen

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    Staff: Mentor

    Re: Finding COM, and inertia please help my answers don't make sense??

    Hi amyparker30! Where are your answers? Where is your working?
     
  4. Apr 20, 2012 #3
    Re: Finding COM, and inertia please help my answers don't make sense??

    ok, my answers are totaly wrong but for COM 1 got (2(2.5+5+2.5+5))/15 = 2

    ICOM=Rotational Inertia = 2^2(2.5+5+5+2.5) = 60

    i bet these are 100% wrong what should I do, my teacher wouldn't help me and the people from class just skipped this question :(
     
  5. Apr 20, 2012 #4
    Re: Finding COM, and inertia please help my answers don't make sense??

    Ok first you need to understand the COM formula and see how it works. Basically you need to specify a coordinate to tell where the COM is. That means you need to find the center of mass in the x direction, y direction, and z direction of the system or object.
    So we start by separating everything in components( x, y and z). Lets do the x direction first.

    We let [itex]d_{nx} [/itex] represent the distance in the x direction for each particle (n=1,2,3,4)
    Then
    [itex]X_{com} = \frac{m_2 d_{2x}+m_3 d_{3x} + m_1 d_{1x}+m_4 d_{4x}}{M}[/itex]
    where M is the total mass. Note that
    [itex]d_{2x}=d_{1x}=0[/itex]
    and
    [itex]d_{3x}=d_{4x}=2 m[/itex]

    Similarly for y:
    [itex] Y_{com} = \frac{m_2 d_{2y}+m_3 d_{3y} + m_1 d_{1y}+m_4 d_{4y}}{M}[/itex]
    Note that
    [itex]d_{2y}=d_{3y}=0[/itex]
    [itex]d_{1y}=d_{4y} = 2 m[/itex]

    Similarly for z:
    [itex] Z_{com} = \frac{m_2 d_{2z}+m_3 d_{3z} + m_1 d_{1z}+m_4 d_{4z}}{M}[/itex]
    But Note that
    [itex]d_{1z} = d_{2z} = d_{3z} = d_{4z} = 0[/itex]
    then
    [itex]Z_{com} = 0[/itex]

    Then at the end you get the COM to be at [itex](X_{com},Y_{com},Z_{com})[/itex]

    Now try to plug in the numbers and see what you get. (Easy!!! =))

    Do the same thing for the next part (moment of inertia), first understand the formula/equation and just follow it slowly.
     
    Last edited: Apr 20, 2012
  6. Apr 20, 2012 #5

    NascentOxygen

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    Staff: Mentor

    Re: Finding COM, and inertia please help my answers don't make sense??

    I think the first part of this question would be a good one for a multiple choice test. :smile:

    By symmetry, the CoM of the two equal masses m1 and m2 is mid-way between them. Likewise, the CoM of the equal mass pair m3 and m4 is mid-way between m3 and m4. And you wouldn't believe our luck :wink: but those two CoM locations coincide! 1OqIj.gif

    So that surely must be the CoM for the 4 bodies.
     
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