Rigid Body - Kinematics
... Preparation for rigid body motion Movement in 3-d + Rotation in 3-d = 6 coordinates Euler angles one of the many possibilities Euler’s theorem ...
... Preparation for rigid body motion Movement in 3-d + Rotation in 3-d = 6 coordinates Euler angles one of the many possibilities Euler’s theorem ...
Phys. Rev. Lett. 93, 073002
... Raman photoassociation of 87 Rb atoms from a Mott insulator phase in an 3D optical lattice. By choosing appropriate parameters for the photoassociation laser fields, we have achieved control over both internal and external degrees of freedom of the molecules. A combination of Feshbach techniques and ...
... Raman photoassociation of 87 Rb atoms from a Mott insulator phase in an 3D optical lattice. By choosing appropriate parameters for the photoassociation laser fields, we have achieved control over both internal and external degrees of freedom of the molecules. A combination of Feshbach techniques and ...
IR Spectroscopy
... The bonds in a given molecule may stretch, bend, or rotate. electrons may move from one orbital to another. These processes are quantized; that is, bonds may stretch, bend or rotate only with certain frequencies, and electrons may jump between orbitals with well defined energy differences. It is the ...
... The bonds in a given molecule may stretch, bend, or rotate. electrons may move from one orbital to another. These processes are quantized; that is, bonds may stretch, bend or rotate only with certain frequencies, and electrons may jump between orbitals with well defined energy differences. It is the ...
Optically polarized atoms_Atomic_Transitions
... • Ratio between system size and wavelength similar to that for atoms • However, high-multipolarity transitions are often important; this is when low-multipolarity transitions are suppressed by selection rules – High-angular-momentum excited states (nuclear isomers) – Isospin-symmetry suppression of ...
... • Ratio between system size and wavelength similar to that for atoms • However, high-multipolarity transitions are often important; this is when low-multipolarity transitions are suppressed by selection rules – High-angular-momentum excited states (nuclear isomers) – Isospin-symmetry suppression of ...
(Chapters 9 and 10) Examples of rotational
... of rotations of an extended object about a fixed axis. Such objects are called rigid bodies because when they rotate they maintain their overall shape. It is just their orientation in space which is changing. Angular Variables: θ, ω, α The variables used to described the motion of “point particles” ...
... of rotations of an extended object about a fixed axis. Such objects are called rigid bodies because when they rotate they maintain their overall shape. It is just their orientation in space which is changing. Angular Variables: θ, ω, α The variables used to described the motion of “point particles” ...
Rotational motion and torque notes
... Rotational Motion The translational motion of a rigid body is analyzed by describing the motion of its center of mass, as well as rotational motion about its center of mass. Each particle of a rotating rigid body has, at any moment, a linear velocity v and a linear acceleration a. The angular veloc ...
... Rotational Motion The translational motion of a rigid body is analyzed by describing the motion of its center of mass, as well as rotational motion about its center of mass. Each particle of a rotating rigid body has, at any moment, a linear velocity v and a linear acceleration a. The angular veloc ...
Document
... Suppose a force F acts on the rigid body. The rigid body rotates through an infinitesimal angle d about a fixed axis. The work dW done by the force while point P moves distance ds is: ...
... Suppose a force F acts on the rigid body. The rigid body rotates through an infinitesimal angle d about a fixed axis. The work dW done by the force while point P moves distance ds is: ...
Rotational Motion
... • The angle in units of radians is the ratio of s and r: • The radian unit has no dimensions; it is the ratio of two lengths. The unit rad is just a reminder that we are using radians for angles. © 2014 Pearson Education, Inc. ...
... • The angle in units of radians is the ratio of s and r: • The radian unit has no dimensions; it is the ratio of two lengths. The unit rad is just a reminder that we are using radians for angles. © 2014 Pearson Education, Inc. ...
Rotational spectroscopy
Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The spectra of polar molecules can be measured in absorption or emission by microwave spectroscopy or by far infrared spectroscopy. The rotational spectra of non-polar molecules cannot be observed by those methods, but can be observed and measured by Raman spectroscopy. Rotational spectroscopy is sometimes referred to as pure rotational spectroscopy to distinguish it from rotational-vibrational spectroscopy where changes in rotational energy occur together with changes in vibrational energy, and also from ro-vibronic spectroscopy (or just vibronic spectroscopy) where rotational, vibrational and electronic energy changes occur simultaneously.For rotational spectroscopy, molecules are classified according to symmetry into spherical top, linear and symmetric top; analytical expressions can be derived for the rotational energy terms of these molecules. Analytical expressions can be derived for the fourth category, asymmetric top, for rotational levels up to J=3, but higher energy levels need to be determined using numerical methods. The rotational energies are derived theoretically by considering the molecules to be rigid rotors and then applying extra terms to account for centrifugal distortion, fine structure, hyperfine structure and Coriolis coupling. Fitting the spectra to the theoretical expressions gives numerical values of the angular moments of inertia from which very precise values of molecular bond lengths and angles can be derived in favorable cases. In the presence of an electrostatic field there is Stark splitting which allows molecular electric dipole moments to be determined.An important application of rotational spectroscopy is in exploration of the chemical composition of the interstellar medium using radio telescopes.