Calculate the moment of inertia of each of the following uniform objects about the axes indicated. Consult Table 9.2 as needed. (a) A thin 2.50-kg rod of length 75.0 cm, about an axis perpendicular to it and passing through (i) one end and (ii) its center, and (iii) about an axis parallel to the rod and passing through it. (b) A 3.00-kg sphere 38.0 cm in diameter, about an axis through its center, if the sphere is (i) solid and (ii) a thin-walled hollow shell. (c) An 8.00-kg cylinder, of length 19.5 cm and diameter 12.0 cm, about the central axis of the cylinder, if the cylinder is (i) thin-walled and hollow, and (ii) solid.
Solution to 31E Step 1 (a) Mass of the rod=2.5kg Length of the rod =75cm=0.75m (i)axis passing through one end I=()ML 2 I=()(2.5x0.75) 2 I=0.469kgm (ii)Axis through centre of rod I=(1/12)ML 2 I=(1/12)(2.5x0.75) 2 I=0.117kgm (iii)For a very thin rod, since the mass is near to the axis, thus the Moment of Inertia =0