Four bodies of masses 5 kg, 2 kg, 3k kg and 4 kg are respectively placed at position (0,0,0), (2,0,0), (0,3,0) and (-2,-2,0). Calculate the moment of inertia about x-axis, y-axis and z-axis.

Explanation

Moment of inertia `I=Sigmamr^(2)`
r-distance between the position of mass for th axis.
`I_(x)=Sigmamy^(2)`
`I_(y)=Sigma mx^(2)`
`I_(x)=m_(1)y_(1)^(2)+m_(2)y_(2)^(2)`
`m_(1)=3, y_(1)=3, m_(2)=4,y_(2)=3`
`I_(x)=3xx(3)^(2)+4xx(2)^(2)=43` unit
`I_(y)=m_(1)x_(1)^(2)+m_(2)x_(2)^(2)`
`m_(1)=3mx_(1)=2,m_(2)=4,x_(2)=2`
`I_(y)=2xx(2)^(2)+4xx(2)^(2)=24` unit
`I_(z)=m_(1)z_(1)^(2)+m_(2)z_(2)^(2)`
`m_(1)=2,z_(1)=2,m_(2)=4,z_(2)=2sqrt(2)`
`I_(2)=2xx(2)^(2)+4xx(2sqrt(2))^(2)`
`=8+32=40` unit.