Physics

An object is formed by attaching a uniform, thin rod with a mass of mr = 6.54 kg and length L = 5.12 m to a uniform sphere with mass ms = 32.7 kg and radius R = 1.28 m. Note ms = 5mr and L = 4R.

1)What is the moment of inertia of the object about an axis at the left end of the rod?
1417.969664

2)If the object is fixed at the left end of the rod, what is the angular acceleration if a force F = 467 N is exerted perpendicular to the rod at the center of the rod?
.8431209992

3)What is the moment of inertia of the object about an axis at the center of mass of the object? (Note: the center of mass can be calculated to be located at a point halfway between the center of the sphere and the left edge of the sphere.)

4)If the object is fixed at the center of mass, what is the angular acceleration if a force F = 467 N is exerted parallel to the rod at the end of rod?
0

5)What is the moment of inertia of the object about an axis at the right edge of the sphere?

Ive been having troubles with this problems for several hours i also talk to a bunch of TAs and even they couldn't help me out. If any one could help me out I would appreciate it. Thanks.

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  1. 1)
    Each shape as a different moment of inertia formula, for the left end of the rod:

    I = (1/3)*M*L^2
    where m = mass of rod

    I = (1/3)*6.54*5.12^2
    I = 57.14

    Now you have to consider the moment of the left end of the sphere too:

    I = (2/5)*M*r^2

    where m = mass of sphere

    I = (2/5)*32.75*1.28^2
    I = 21.46

    but you also have to consider the distance from the center of mass too so:

    I= 21.46 + 32.7*(6.54+1.28)^2
    I = 2021.14

    Answer:
    M.I of rod + M.I of sphere
    21.46+2021.14 = ??

    2)
    (L/2)*F = M <-- torque
    L = length of rod
    F = Force

    Once you find M

    angular acceleration= M/(21.46+2021.14 )
    (its divided by what you get in the first problem)

    4) #4 is correct

    try #3 and #4 by yourself, if you have problems post here again.

    Here are links to formulas for M.I of different shapes.. Hopefully your prof provides formula sheets for this..

    http://www.engineersedge.com/mechanics_machines/mass_moment_of_inertia_equations_13091.htm

    http://hyperphysics.phyastr.gsu.edu/hbase/mi2.html

    http://hyperphysics.phyastr.gsu.edu/hbase/isph.html

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  2. Every number I have posted is correct. I'm just having problems with 3 and 5. I have access to all of those equations too but i still can't seem to find the right answer. I've been trying for hours and like I said no one i have talked to knows how to do it even my TAs.

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