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

label Physics
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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) 2.70 2.10 4.50 2.30
(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.
Jun 10th, 2015

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

Jun 10th, 2015

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Jun 10th, 2015
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Jun 10th, 2015
Nov 20th, 2017
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