We investigate the coupling of the superfluid of a neutron star with the solid crust arising from the scattering of individual nuclei in the inner crust with dynamical vortex lines of the superfluid. Such interactions generate quantized Kelvin mode vortex oscillations (kelvons). We calculate the rate of kelvon production and the consequent drag produced on the superfluid. The coupling is sufficiently strong to permit glitch spin-up time scales less-than-or-similar-to 60 times the rotation period. Catastrophic vortex-unpinning events are therefore capable of producing giant glitches with rapid spin-ups on the scale observed in the Vela pulsar.