The center of mass is at (0.068a,0) Consider the model of the water molecule H2O

Question

The center of mass is at (0.068a,0)

Consider the model of the water molecule H2O discussed in Homework 1. Assume that the mass of oxygen atom is 16 times that of a hydrogen atom Calculate the moment of inertia of the molecule about an axis perpendicular to the plane of the hydrogen and oxygen atoms, ami passing through the oxygen atom. Calculate the moment of inertia of the molecule about an axis perpendicular to the plane of the hydrogen and oxygen atoms, and passing through the center of mass of the molecule.

Explanation / Answer

a) I = sum of mr^2, where r is the distance from the axis for each atom
O is on the axis so its r=0
both Hs have r=a
so I=2m a2, where m is the mass of the hydrogen atom

b) now we use parallel axis theorem I=Icenter of mass + Md2,where M is the total mass and d is the length of the shift

so here I center of mass = I - Md2=2ma2-(16+1+1)m(0.068a)2

so I center of mass= (2-18*0.0682)ma2=1.917 m a2

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