Calculate moment of inertia with respect to rotational axis xx' in following figures a and b.

Explanation

a. `I_(xx')=m_(1)x_(1)^(2)+m_(2)x_(2))`
`m_(1)=4,x_(1)=0.3,m_(2)=1,x_(2)=0.8`
`I_(xx')=4xx(0.3)^(2)+1xx(0.8)^(2)`
`=4xx(0.09)+1xx(0.64)`
`=0.36+0.64=1kgm^(2)`
b. `I_(xx')=m_(1)y_(1)^(2)+m_(2)y_(2)^(2)+m_(3)y_(3)^(2)`
`m_(1)=4, m_(2)=2, m_(3)=3, y_(1)=3`
`y_(2)=-2, y=-4`
`I_(xx')=4xx(3)^(2)+2xx(-2)^(2)+3xx(-4)^(2)`
`=4xx9+2xx4+3x16`
`=36+8+48=92kgm^(2)`