  This Letter reports on the first measurements of transverse momentum
dependent flow angle $\Psi_n$ and flow magnitude $v_n$ fluctuations, determined
using new four-particle correlators. The measurements are performed for various
centralities in Pb-Pb collisions at a centre-of-mass energy per nucleon pair of
$\sqrt{s_{\rm NN}}$ = 5.02 TeV with ALICE at the CERN Large Hadron Collider.
Both flow angle and flow magnitude fluctuations are observed in the presented
centrality ranges and are strongest in the most central collisions and for a
transverse momentum $p_{\rm T}>2$ GeV/$c$. Comparison with theoretical models,
including iEBE-VISHNU, MUSIC, and AMPT, show that the measurements exhibit
unique sensitivities to the initial state of heavy-ion collisions.
