Sphere Let us find the moment of inertia of a uniform solid sphere of radius a and mass m about an axis (the z-axis) passing through the center. We divide the sphere into thin circular discs, as shown in Figure 8.3.3. The moment of inertia of a representative disc of radius y, from Equation 8.3.7, isy²dm. But dm = pay² dz; hence, 2 4 8 I = py* dã = Enpa – z) dữ = pa 15 wa (8.3.8) The last step in Equation 8.3.8 should be filled in by the student. Because the mass m is given by we have m = na ³ p παρ I₂ = ² ma² for a solid uniform sphere. Clearly also, I₂ = ly = Iz (8.3.9) (8.3.10)

Sphere Let us find the moment of inertia of a uniform solid sphere of radius a and mass m about an axis (the z-axis) passing through the center. We divide the sphere into thin circular discs, as shown in Figure 8.3.3. The moment of inertia of a representative disc of radius y, from Equation 8.3.7, isy²dm. But dm = pay² dz; hence, 2 4 8 I = py* dã = Enpa – z) dữ = pa 15 wa (8.3.8) The last step in Equation 8.3.8 should be filled in by the student. Because the mass m is given by we have m = na ³ p παρ I₂ = ² ma² for a solid uniform sphere. Clearly also, I₂ = ly = Iz (8.3.9) (8.3.10)