# Example 10.5
MKS(mm, mm^4)
r = 25 mm
Ix_prime = (1/4) * pi() * r^4
a = pi() * r^2
dy = 75 mm
Ix_circ = Ix_prime + a * dy^2
Ix_rect = (1/12) * 100 mm * (150 mm)^3 + (100 mm) * (150 mm) * (75 mm)^2
Ix = Ix_rect - Ix_circ

# Example 10.6
MKS(mm, mm^4)
ix_rect_a = (1/12) * (100 mm) * (300 mm)^3 + (100 mm) * (300 mm) * (200 mm)^2
iy_rect_a = (1/12) * (300 mm) * (100 mm)^3 + (100 mm) * (300 mm) * (250 mm)^2
ix_rect_b = (1/12) * (600 mm) * (100 mm)^3
iy_rect_b = (1/12) * (100 mm) * (600 mm)^3
ix_rect_d = (1/12) * (100 mm) * (300 mm)^3 + (100 mm) * (300 mm) * (200 mm)^2
iy_rect_d = (1/12) * (300 mm) * (100 mm)^3 + (100 mm) * (300 mm) * (250 mm)^2
ix = ix_rect_a + ix_rect_b + ix_rect_d
iy = iy_rect_a + iy_rect_b + iy_rect_d

# Example 10.8
MKS(mm, mm^4)
ixy_rect_a = 0 mm^4 + (300 mm) * (100 mm) * (-250 mm) * (200 mm)
ixy_rect_b = 0
ixy_rect_d = 0 + (300 mm) * (100 mm) * (250 mm) * (-200 mm)
ixy = ixy_rect_a + ixy_rect_b + ixy_rect_d

# Example 10.9
MKS(mm, mm^4, deg)
ix = 2.90e9 mm^4
iy = 5.60e9 mm^4
ixy = -3.00e9 mm^4
tan2q = -ixy / ((ix - iy) / 2)
q = atan(tan2q) / 2
imax = (ix + iy)/2 + sqrt((ix - iy)^2/2 + ixy^2)
imin = (ix + iy)/2 - sqrt((ix - iy)^2/2 + ixy^2)

# Example 10.13
MKS(mm, mm^4, deg)
rd = 8000 kg/m^3
vd = pi() * (0.25 m)^2 * 0.01 m
md = rd * vd
d = 0.25 m
r= 0.25 m
iod = (1/2) * md * r^2 + md * d^2
d = 0.25 m
r= 0.125 m
mh = rd * pi() * (0.125 m)^2 * 0.01 m
ioh = (1/2) * mh * r^2 + mh * d^2
io = iod - ioh

# Example 10.14
FPS(slug, slug ft^2)
m1 = 10 lbm
i1 = (1/3) * m1 * (2 ft)^2
i2 = (1/12) * m1 * (2 ft)^2 + m1 * (1 ft)^2
i3 = (1/12) * m1 * (2 ft)^2 + m1 * (2 ft)^2
i4 = i2 + i3
ybar = (1 ft * m1 + 2 ft * m1) / (2 * m1)
ig = i4 - (20 lbm) * (1.5 ft)^2

# Homework Problems:

TBD