Science
Four objects are held in position at the corners of a rectangle by light rods as

Question Description

Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. (The mass values are given in the table.)

m1 (kg) m2 (kg) m3 (kg) m4 (kg) 
2.702.104.502.30
(a) Find the moment of inertia of the system about the x-axis.
 kg · m2

(b) Find the moment of inertia of the system about the y-axis.
 kg · m2

(c) Find the moment of inertia of the system about an axis through O and perpendicular to the page.

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Final Answer

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moment of inertia =Sum[ mass x distance^2] 

where the distance is the distance from the chosen rotation axis 

a) here, moment of inertia = 

(2.7+2.1+4.5+2.3)3^2 = 104.4kgm^2 

because each mass is 3 m from the x axis 

b) now we consider distances from the y axis; each mass is 2m from the y axis: 

I=(2.7+2.1+4.5+2.3)2^2=46.4 kgm^2 

c) the distance from the rotation axis is now found from the pythagorean theorem 

distance^2=2^2+3^2=13 

I=(2.7+2.1+4.5+2.3)*13=150.8 kgm^2

Please let me know if you need any clarification. I'm always happy to answer your questions.

Fatin Menhaz (1755)
UC Berkeley

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