Your favorite flying sport disk can be approximated as the combination of a thin

Question

Your favorite flying sport disk can be approximated as the combination of a thin outer hoop and a uniform disk, both of diameter Dd 0.273 m as shown in the figure below. The mass of the hoop part is m 0.120 kg and the mass of the disk part is md 0.055 kg. You would like to make a boomerang that has the same total moment of inertia, around its center, as the sport disk. The boomerang is to be constructed in the shape of an "X," which can be approximated as two thin uniform rods joined at their midpoints. If the total mass of the boomerang is to be mb-0.235 kg, what must be the length Lb of the boomerang? Number L-47 0.273 m cross-sectional view

Explanation / Answer

Moment of inertia of disc system

I=(1/2)mdRd2 + mhRd2 =(1/2)*(0.055)*(0.273/2)2 + 0.12*(0.273/2)2

I=2.748*10-3 Kg-m2

Moment of inertia of boomerang

I=(1/12)mbLb2 =2.748*10-3

=>(1/12)*0.235 *Lb2=2.748*10-3

Lb=0.3746 m

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