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4 Point masses form a body - Inertia & Rotational Kinetics

  1. Nov 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Four point masses form a rigid body (they are connected by massless rigid rods) given the positions M1= 3kg (2m, 4m, 0m) M2= 2kg (1m, -4m, 0m) M3= 1kg (10m, 2m, 0m) M4= 5kg (-5m, 2m, 0m)
    Find:
    A) Moment of inertia of this system when it rotates about x axis
    B) Moment of interia of this system when it rotates about y axis
    C) Total rotational kinetic energy in the (A) case when ω= 4 rad/s
    D) Total rotational kinetic energy in the (B) case when ω= 4 rad/s

    2. Relevant equations

    Rotational K = 1/2Iω2

    3. The attempt at a solution

    I'm really terrible at things with center of mass :confused: but I believe we'd have to somehow find the total systems Center of Mass in order to find it's moment(s) of Inertia. However I don't know how to do this with the different axis' (x & y). And as I know from the formula, I can't solve for Rotational Kinetic energy without them :frown:

    Help?
     
  2. jcsd
  3. Nov 7, 2012 #2

    SteamKing

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    Do you know how to calculate the center of mass of a body knowing the components of the body and the c.m. of each component? Do you know the formula for calculating center of mass? In cases such as this, try drawing a picture showing each component mass and its location from the origin.

    You will have to deal with this before proceeding to calculate moment of inertia for the composite body.
     
  4. Nov 7, 2012 #3
    I have the general idea, and I have drawn a diagram. I believe the formula is Xcm(M)=x1m1+x2m2+x3m3+x4m4 where M is the total mass and Xcm is the centre of mass in the x direction. But once I find this how do I get the moment of inertia for rotating around the x axis? Do I just use Xcm in the formula I=Icm + MD2 (parallel axis theorem?) And if so what would be D because none of them fall right on the x axis...
     
  5. Nov 7, 2012 #4

    SteamKing

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    D is going to be the distance of the c.o.m. of each point mass from the x-axis. (Hint: remember the Pythagorean Theorem). Calculate MOI about the origin for the body, then transfer the MOI from the origin to the c.o.m. using the parallel axis theorem.
     
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