Rotational frequency in the context of "Turn (unit)"

Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or r⋅min) is a unit of rotational speed (or rotational frequency) for rotating machines.One revolution per minute is equivalent to ⁠1/60⁠ hertz.

In physics, angular frequency (symbol ω), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves).Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity.

Angular frequency can be obtained by multiplying rotational frequency, ν (or ordinary frequency, f) by a full turn (2π radians): ω = 2π rad⋅ν.It can also be formulated as ω = dθ/dt, the instantaneous rate of change of the angular displacement, θ, with respect to time, t.

Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The rotational spectrum (power spectral density vs. rotational frequency) 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 tops, linear molecules, and symmetric tops; 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.