![]() The moment of inertia about the z axis is the sum of the moments of inertia about the other two axes. This theorem applies to planar molecules. Should be familiar from the tutorial on collisions as the reduced mass. Where r is the bond length, and atom 2 at Putting the origin at the centre of mass, atom 1 is at Suppose the z-axis is aligned along the bond direction and the atoms are at z 1 and z 2. We now calculate the moment of inertia of a diatomic molecule about an axis perpendicular to the bond (this is one of the principal components - see later). The consequence the natural moment of inertia of a molecule is about an axis passing through the centre of mass, and it is straightforard to calculate it for any other axis. The result follows because the two central sums are zero from the definition of the centre of mass. Where M is the mass of the molecule and d the distance of the axis from the centre of mass. The moment of inertia about any other axis perpendicular to this may be found to be Thus the moment of inertia is minimised if the axis passes through the centre of mass of the molecule. The moment of inertia may be minimised with respect to the position of the axis, for example ![]() Where r i is the distance of atom i from the axis of rotation.Ĭonsider a molecule rotating about an axis parallel to the z-axis with fixed x and y coordinates. ![]() In chemistry we are most interested in the rotation of molecules, which are essentially made up of point masses, giving it measures the inertial towards angular acceleration. The moment of inertia of a single particle rotating about a centre was introduced in the tutorial on circular motion ![]()
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