Fast-camera observations of distinctive forked patterns caused by disintegrating molten metal particles in the JET tokamak are presented. These patterns are characterised by repeated splitting of particles into pairs of equally sized sub-particles; such regularity can only be explained by the two-lobed bifurcations of liquid droplets rotating with velocities in excess of 105s-1. These speeds are consistent with longstanding theories of particle spin-up in magnetized plasmas but are at least two orders of magnitude greater than any previous measurement of rotating particles in plasmas. The verification of spontaneous liquid particle spinning processes in plasmas has widespread implications in astrophysics, particularly for the explanation of anomalous microwave radiation and its associated measurements of the cosmic magnetic field. Furthermore, by incorporating the rotation of droplets into the dust tracking code DTOKS, the fast-camera observations are reliably replicated in JET and predictions for future droplet behaviour in next-generation tokamaks can be made. These simulations show that the higher magnetic fields, plasma temperatures and densities of ITER will enhance the breakup process, thus protecting the core plasma from acute impurity deposition and subsequent disruption events and providing significant operational benefits.