3. A diatomic molecule is accurately modeled as two point masses of magnitude m separated by total distance d (the atomic spacing). If we place the center of mass of this system at the origin of our coordinate system, and the two nuclei are on the x-axis, what is the kinetic energy of the molecule if it rotates at frequency omega about (1) the z-axis? (2) the y-axis? (3) the x-axis?
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Rotational kinetic energy = (1/2) I w^2
I=rotational inertia
w=omega
Ix =rotational inertia about the x-axis = 0
ly =rotational inertia about the y-axis
lz =rotational inertia about the z-axis
Iy=Iz= m(d/2)^2 + m (d/2)^2 =(m d^2)/2
(1) and (2) are the same KE = m d^2 w^2
(3) is KE = 0
I=rotational inertia
w=omega
Ix =rotational inertia about the x-axis = 0
ly =rotational inertia about the y-axis
lz =rotational inertia about the z-axis
Iy=Iz= m(d/2)^2 + m (d/2)^2 =(m d^2)/2
(1) and (2) are the same KE = m d^2 w^2
(3) is KE = 0