A diatomic gas molecule has a mass of 2.63 x 10 -26 kg and a rotational inertia

Question

A diatomic gas molecule has a mass of 2.63 x 10-26 kg and a rotational inertia of 1.28 x 10-46 kg

A diatomic gas molecule has a mass of 2.63 times 10-26 kg and a rotational inertia of 1.28 times 10-46 kg·m2 about an axis through the center of the line joining the atoms and perpendicular to that line. Suppose the center of mass of the molecule has a translational speed of 531 m/s and the molecule has a rotational kinetic energy that is of the translational kinetic energy of its center of mass. What then is the molecule's angular speed about the center of mass?

Explanation / Answer

0.5*m*v^2 = 0.5*I*w^2

==> w = sqrt(m*v^2/I)

==>w = v*sqrt(m/I) = 531*sqrt(2.63*10^-26/1.28*10^-46)

==> w = 7.61*10^12 rad/s

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