08.2 Three square plates, each 1.0 m on a side and with the same uniform density

Question

08.2 Three square plates, each 1.0 m on a side and with the same uniform density, are connected as shown. Each plate has mass 2.0 kg. Find the moment of inertia of the system about (a) axis A, (b) axis B, (c) axis C, and (d) an axis perpendicular to the plane of the plates through point O. [Hint:Use the moments of inertia in Table 9.2 of the text and the parallel axis theorem.]

08.2 Three square plates, each 1.0 m on a side and with the same uniform density, are connected as shown. Each plate has mass 2.0 kg. Find the moment of inertia of the system about (a) axis A, (b) axis B, (c) axis C, and (d) an axis perpendicular to the plane of the plates through point O. Hint: Use the moments ofinertia in Table 9.2 of the text and the parallel axis theorem.1

Explanation / Answer

the moment of inertia about an edge of a square is

1/3 * m * a^2

a) axis A

for 1 and 2

1/3 * m * a^2 + 1/3 * m * a^2

for 3

1/3 * m * a^2 + m*a^2 ( from parallel axis theorem )

that is 4/3 m * a^2

therefore total moment of inertia I = 2/3 m *a^2 + 4/3 m * a^2

I = 2 * m * a^2

I = 4 kg-m^2

b)

I = 3 * (1/3 m * a^2 )

I = 2 kg-m^2

c)

I = 1/3 m * a^2 + 2 * (4/3 m * a^2)

I = 6 kg-m^2

d)

the moment of inertia through one corner is (2/3) m * a^2

for the three plates

I = 3 * (2/3 * m * a^2)

I = 4 kg-m^2

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