A variety of transition-selective solid-state N-14 (1 = 1)NMR techniques are demonstrated for the first time to be useful for quantitatively describing;slow molecular motions in the solid state. These techniques are validated by quantitative measurements of molecular reorientation by tetrahedral jumps in hexamethylenetetramine (HMT). A new four-site magnetization-exchange model, capable of being generalized to n-sites, which includes the effects of spin-lattice relaxation is developed. This model provides the limiting conditions under which the orientation dependence of spin-lattice relaxation values T-1 can be safely neglected. The model is used to analyze results from a frequency-selective DANTE train used to burn a hole in the spectrum, that provide a direct indication of the existence of 4-site exchange. The measured correlation time for the motion in HMT of 103+/-6 ms at room temperature agrees well with previous studies by other techniques. In a novel application to molecular dynamics, the repeated hole-burning pulse trains of the SINK experiment are used to measure a magnetization recovery time constant due to N-14 spin-lattice relaxation in HMT of 0.99 +/- 0.12 s. Both experiments employ frequency-selective as well as transition-selective radio frequency pulses on a relatively small frequency region (<100 kHz) of the entire quadrupolar powder pattern of HMT (NQCC=4.414 MHz, eta=0). The Hahn spin-echo used for detection can be understood in terms of the fictitious spin-1/2 formalism. Quantitative dynamical information is obtained from measurements at only one frequency position of a wide inhomogeneously broadened powder pattern. Because we are operating in this unusual regime, the sensitivity can be significantly improved by replacing the DANTE hole-burning train with a series of pi/2 pulses that saturate all observable magnetization. Results from such an experiment compare well with those obtained using DANTE trains.