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Chuck W.
Apr 23, 2014

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#

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