The Following problems will lead you to find the moment of inertia of a uniform thick...

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The Following problems will lead you to find the moment of inertia of a uniform thick spherical shell of inner radius b and mass M. (The moment of inertia of a thin spherical shell is I = 2MR/3). 8) What is the volume of the thick shell of inner radius a, outer radius b and mass M? a) 4(b - a)/3 difference of volumes of spheres of radii b and a. 9) What is the volume dV of a thin spherical layer of radius r and thickness dr? a) 4r dr 10) What is the mass dM of this layer? a) 3Mr dr/(b a) Ratio of the above two 11) What is dI, the contribution of this layer to the moment of inertia of the thick shell? a) 2Mr dr/(b a) dM times 2r/3 12) What is the moment of inertia of the thick shell? a) M(b5 a )/(b a) Integral of the above The Following problems will lead you to find the moment of inertia of a uniform thick spherical shell of inner radius b and mass M. (The moment of inertia of a thin spherical shell is I = 2MR/3). 8) What is the volume of the thick shell of inner radius a, outer radius b and mass M? a) 4(b - a)/3 difference of volumes of spheres of radii b and a. 9) What is the volume dV of a thin spherical layer of radius r and thickness dr? a) 4r dr 10) What is the mass dM of this layer? a) 3Mr dr/(b a) Ratio of the above two 11) What is dI, the contribution of this layer to the moment of inertia of the thick shell? a) 2Mr dr/(b a) dM times 2r/3 12) What is the moment of inertia of the thick shell? a) M(b5 a )/(b a) Integral of the above