Question

Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Picture Object and axis Thin rod about center ML2 Cylinder or disk MR about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Маг | Solid sphere, about diameter MR2 Plane or slab about edge MaSpherical shell, about diameter MR2 2. b. A very thin, flat, uniform slab has a width of W, a height of H, and a total mass of M Treating the slab as essentially a sheet of mass-distributed uniformly over its area-do the following (i) Use integration to prove that the slab's center of mass is located at its center point (i.e. W/2 from either side and H/2 from top and bottom) (ii) Now use integration to calculate /m, the moment of inertia of the slab about an axis through the center of mass (and that axis is parallel to the sides). Compare your result to that given on page 300 of the textbook (iii) Now, without integrating (ie. by using the Parallel Axis Theorem and the previous result), calculate !side, the moment of inertia of the slab about an axis along one side of the slab (and parallel to that side) Again, compare your result to that given on page 300 of the textbook

Answer 1