- 8 1 Center Of Mass Of A Rigid Body 325 Dz A Do Do Figure 8 1 1 Coordinates For Calculating The Center Of Mass Of A Hemis 1 (124.59 KiB) Viewed 26 times
8.1 Center of Mass of a Rigid Body 325 dz a do do Figure 8.1.1 Coordinates for calculating the center of mass of a hemisphere. а X Similarly, if the body has a line of symmetry, it is easy to show that the center of mass lies on that line. The proof is left as an exercise. a -Z Solid Hemisphere To find the center of mass of a solid homogeneous hemisphere of radius a, we know from symmetry that the center of mass lies on the radius that is normal to the plane face. Choosing coordinate axes as shown in Figure 8.1.1, we see that the center of mass lies on the z-axis. To calculate Zem we use a circular element of volume of thickness dz and radius=(a* - 23,12, as shown. Thus, dv = (a? - Z)dz (8.1.7) Therefore, paza* – xº)dz (8.1.8) Spala? – zº)dz 2 = - Z Zom a