# Question e35ee

Apr 23, 2014

The moment of inertia is calculated from the sum

$I = {m}_{1} \times {r}_{1}^{2} + {m}_{2} \times {r}_{2}^{2} + {m}_{3} \times {r}_{3}^{2}$

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

${r}_{i}^{2} = {\left({x}_{i} - {x}_{c m}\right)}^{2} + {\left({y}_{i} - {y}_{c m}\right)}^{2}$

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#