Question

Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center | Cylinder or disk, about center MR ML2 Thin rod, about end ML Cylindrical hoop. MR2 about center | Solid sphere, about diameter Маг Plane or slab, about center Ma2 MR Plane or slab, about edge Ma2 Spherical shell, about diameter MR2 1. b. A very thin, straight, uniform rod has a length L and a total mass M. Treating the rod as essentially a line segment of mass (distributed uniformly), do the following: Use integration to prove that the rod's center of mass is located at its center point (ie. L/2 from either end) mass (and that axis is perpendicular to the rod). Compare with the result given on page 300 of the textbook with the previous result-to calculate lend the moment of inertia of the rod about an axis through one end of (ii) Now use integration to calculate m the moment of inertia of the rod about an axis through that center of (iii) Now use two different methods-first by direct integration, then by using the Parallel Axis Theorem along the rod (and that axis is perpendicular to the rod). Compare with the result given on page 300 of the textbook

Answer 1