Consider a hollow sphere...

Question

Consider a hollow sphere of radius r=a, and mass M, distributed uniformly over the surface of the sphere. Using integration of spherical coordinates, find:

a. the surface area of the sphere

b. the center of mass of the curved area of the upper hemisphere

c. the moment of inertia of the sphere about an axis passing through the diameter (along the z axis)

Answer 1

area=4/3r^3π

Mass cntr.

Mx=∫ ∫ yρ(x,y)dA

R

My=∫ ∫ xρ(x,y)dA

R

Inertia

Mx=∫ ∫ (y)ρ(x.y)dA

R

My=∫ ∫ (x)ρ(x,y)dA

R