A thin, rectangular sheet of metal has mass ?M? and sides of length ?a? and ?b?. 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.

Solution 55E Step 1: The rectangular sheet of mass “M” and sides “a” and “b” has a moment of inertia, Ic= m [a + b ] about the centre. 12 Step 2: Now we want to get the moment of inertia at one of the corner. To do this, let’s calculate the distance of the corner from the centre. The diagonal distance from the centre to the corner is, a 2 b 2 r = (2) + (2) = 1 a + b . 2