A thin, rectangular sheet of metal has a mass of 880 grams and sides of 23 cm an

Question

A thin, rectangular sheet of metal has a mass of 880 grams and sides of 23 cm and 12 cm respectively. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet A thin, rectangular sheet of metal has a mass of 880 grams and sides of 23 cm and 12 cm respectively. Use the parallel-axis theorem to calculate the moment of inertia of the sheet for an axis that is perpendicular to the plane of the sheet and that passes through one corner of the sheet

Explanation / Answer

The moment of inertia about an axis through the centre and perpendicular to the lamina is:
M(a^2 + b^2) / 12.

If h is the length of a semi-diagonal:
h^2 = (a/2)^2 + (b/2)^2
= (a^2 + b^2) / 4.

By the parallel axis theorem, the moment of inertial about an axis through the corner is:
M(a^2 + b^2) / 12 + Mh^2
= M(a^2 + b^2)(1/12 + 1/4)
= M(a^2 + b^2) / 3.

=(0.88 kg ) (0.23 ^2 + 0.12 ^2 ) / 3

=0.0197 kg.m^2

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