Include this assignment sheet in your report Determine the t

Include this assignment sheet in your report. Determine the three mass products of inertia with respect to xyz coordinate system shown. Density rho = 7850 kg/m^3

Solution

The problem can be divided into 4 parts:
a. find MOI of 50*80*50 block
b. find MOI of 70*80*12 block
c. find MOI of 40*80*50 block
d. find MOI of 24*40 cylinder

a. MOI about line passing through the centre = m1/12(80^2 + 50^2)
MOI about xyz = m1/12(6400+2500) + m1*(40^2 + 25^2)
now, m1 = rho(50*80*50) = 1.57kg
MOI = 1164.41 + 3494.25 = 4,657.66 kg mm^2

b. MOI about line passing through the centre = m2/12(80^2 + 70^2)
MOI about xyz = m2/12(6400+4900) + m2*(40^2 + 85^2)
now, m2 = rho(70*80*12) =0.527 kg
MOI = 496.25 + 4650.775 = 5147.025 kg mm^2

c. MOI about line passing through the centre = m3/12(80^2 + 40^2)
MOI about xyz = m3/12(6400+1600) + m1*(40^2 + 140^2)
now, m3 = rho(40*80*50) = 1.256 kg
MOI = 837.33 + 26627.2 = 27464.53 kg mm^2

d. MOI about line passing through the centre = m4/24(3*24^2 + 40^2)
MOI about xyz = m4/24(1728+1600) + m4*(40^2 + 140^2)
now, m4 = rho(pi*24^2*20) = 0.283kg
MOI = 39.24 + 5999.6 = 6038.84 kg mm^2

Net MOI + 1 + 2 + 3 - 4 = 3.123 kg m^2