Question

Question #e35ee

Answer 1

The moment of inertia is calculated from the sum

`I=m_1timesr_1^2 + m_2timesr_2^2 + m_3timesr_3^2`

where `r_i` is the distance of point mass `i` from the center of mass of the three points. The square of each distance is calculated in Cartesian coordinates as

`r_i^2=(x_i-x_(cm))^2+(y_i-y_(cm))^2`

The center-of-mass coordinates (`x_(cm),y_(cm))` can be found from the simple formula below if you know the masses of the three points and their coordinates in any (x,y) plane.

`x_(cm) = (m_1 timesx_1 + m_2 times x_2 + m_3 times x_3)/(m_1+m_2+m_3`

`y_(cm) = (m_1 timesy_1 + m_2 times y_2 + m_3 times y_3)/(m_1+m_2+m_3`