Kinetic energy of rotation

The Hamiltonian in this problem contains only the kinetic energy of rotation no potential energy is present because the molecule is undergoing unhindered "free rotation". The angles 0 and (j) describe the orientation of the diatomic molecule s axis relative to a laboratory-fixed coordinate system, and p is the reduced mass of the diatomic molecule p=mim2/(mi+m2). 

The kinetic energy of rotation of the electron around its proper axis equals the kinetic energy of the positron. The total rotational energy is then... 

The internal energy of a substance does not include any energy that it may possess as a result of its macroscopic position or movement. Rather it refers to the energy of the molecules making up the substance, which are in ceaseless motion and possess kinetic energy of translation except for monatomic molecules, they also possess kinetic energy of rotation and of internal vibration. The addition of heat to a substance increases this molecular activity, and thus causes an increase in its internal energy. Work done on the substance can have the same effect, as was shown by Joule. 

Then, the classical expression for the kinetic energy of rotation takes the form ... 

Energy of rotation n. If a mass whose moment of inertia about an axis is J, rotates with angular velocity co about this axis, the kinetic energy of rotation will be... 

The first three ( diagonal ) terms have a clear interpretation. These are the kinetic energy of the centre of mass, the kinetic energy of rotation, and the kinetic energy of vibrations. The three further terms ( non-diagonal ) denote the roto-translational, vibro-translational and vibro-rotational couplings. 

Component of angular momentum perpendicular to intemuclear axis = mjh. Kinetic energy of rotation Tj = J J + )tp-/2I. 

As usual it will be assumed that the canonical partition function Q of the system may be written as the product of an internal partition function which does not depend on the configurational coordinates (but includes the contributions of the internal degrees of freedom and the kinetic energy of rotation and translation) and a configurational partition function... 

There is another potential failure mode that must be considered in design of fan impeller blades, and that is impact failure if the blade were to strike an obstacle. Assume impact at the tip of the blade. Then the blade can be taken as a cantilever beam loaded at the end. Assume a uniform cross section, and assume the kinetic energy of rotation of the blade before impact is totally absorbed as strain energy in bending the beam. 

Consider a diatomic molecule, rotated around an axis passing through the CM (Figure 1.17). The problem is to express the Ml of this molecule and the corresponding kinetic energy of rotation through its parameters, which are supposed to be known (for instance, from the reference hterature). hi the figure, the masses of two atoms of the molecule are marked by letters m and m2, and the letter d denotes an interatomic distance... 

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