  Fast (sub-second) spectroscopy with high spectral resolution is of vital
importance for revealing quantum chemistry kinetics of complex chemical and
biological reactions. Fourier transform (FT) spectrometers can achieve high
spectral resolution and operate at hundreds of ms time scales in rapid-scan
mode. However, the linear translation of a scanning mirror imposes stringent
time-resolution limitations to these systems, which makes simultaneous high
spectral and temporal resolution impossible. Here, we demonstrate an FT
spectrometer whose operational principle is based on continuous rotational,
rather than linear, motion of the scanning mirror, decoupling the spectral
resolution from the temporal one. This enables 0.5 cm${}^{-1}$ resolution on
sub-ms time scales. Furthermore, we show that such rotational FT spectrometers
can perform dual-comb spectroscopy with a single comb source, since the
Doppler-shifted version of the comb serves as the second comb. In this way, we
combine the advantages of dual-comb and FT spectroscopy using a single quantum
cascade laser frequency comb as a light source. Our technique does not require
any diffractive or dispersive optical elements and hence preserve the
Jacquinot's-, Fellgett's-, and Connes'-advantages of FT spectrometers. The
system supports a large optical bandwidth from visible to THz frequencies. The
combination of a rotational delay line with collimated coherent or non-coherent
light sources pave the way for FT spectrometers in applications where high
speed, large optical bandwidth, and high spectral resolution are desired.
