The axial magneticeffect, i.e., the generation of an energy current parallel to an axial magnetic field coupling with opposite signs to left-and right-handed fermions, is a nondissipative transport phenomenon intimately related to the gravitational contribution to the axial anomaly. An axial magnetic field emerges naturally in condensed matter in so-called Weyl semimetals. We present a measurable implementation of the axial magnetic effect. We show that the edge states of a Weyl semimetal at finite temperature possess a temperature dependent angular momentum in the direction of the vector potential intrinsic to the system. Such a realization provides a plausible context for the experimental confirmation of the elusive gravitational anomaly. Anomalies have played an important role in the construction of consistent quantum field theory (QFT) and string theory models. Among them, the most intensively investigated case is that of the axial anomaly, which is responsible for the decay of a neutral pion into two photons [1]. Similarly, in a curved space, gravitational anomalies [2] can occur and mixed axialgravitational anomalies give rise to very interesting predictions as to the decay of the pion into two gravitons. While the former phenomenon is by now well established, experimental settings providing evidence of the gravitational anomaly are lacking. More recently anomalies are starting to play an interesting role as being responsible for exotic transport phenomena in QFT in extreme conditions. In the context of the quark-gluon plasma [3] it has become clear in recent years that, at finite temperature and density, quantum anomalies give rise to new nondissipative transport phenomena.The recognition of the role of topology in the classification of condensed matter systems started a long time ago with the prototypical example set by liquid helium [4]. The low energy excitations of He 3 are described by Dirac fermions, which made the system an interesting analog to study high energy phenomena. In this century, the advent of new materials (graphene, topological insulators and superconductors [5,6], and Weyl semimetals) whose low energy electronic properties are described by Dirac fermions in one, two, or three spatial dimensions has enlarged and widened the analogy between high energy and condensed matter. Simultaneously, new experiments on the quark-gluon plasma and recent developments in holography have opened an unexpected scenario where high energy and condensed matter physics merge. In this Rapid Communication we propose a condensed matter scenario for the experimental realization of the gravitational anomaly.The most commonly cited example of the new nondissipative transport phenomena occurring in the quark-gluon plasma is the chiral magnetic effect [7], which refers to the generation of an electric current parallel to a magnetic field whenever an imbalance between the number of right-and left-handed fermions is present. Another interesting example is the axial magnetic effect (AME), which is associated with the ...