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Moments of Inertia Ranking

Three pairs of balls are connected by very light rods as shown in the figure.

Rank in order, from smallest to largest, the moments of inertia I1, I2, and I3 about axes through the centers of the rods.

=I2, I1, I3

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Comments ( 2 )

  1. 2<1<3

    "if m1 and m2 are the two mass which are separated by distanceR by fixed mass less rod , are rotated on the axispassing through mid point
    I = m1 ( R/2 )2 + m2 ( R/2)2
    for 1 we have
    I = m ( R/2 ) 2 +m ( R/2 ) 2 = 1/2 mR2
    for 2 we have
    I = 2m ( R/4 ) 2 + m ( R/4 ) 2 =3 /16 m R2
    for 3 we have
    I= m/2 ( R ) 2 + m/2 ( R) 2 = mR2
    so we have the order 2<1<3"

  2. In the response answer, for I3, is that MR(2) or MR^2

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