The authors study the Kuramoto model with inertia given by \[ \ddot{\theta}_i+\dot{\theta}_i=\omega_i+\frac{2K}{n}\sum_{j=1}^n a_{ij}^n\sin{(\theta_j-\theta_i)}, \] where \(K\) is the coupling strength and \(a_{ij}^n\) is the adjacency matrix of one from a convergent sequence of graphs. The intrinsic frequencies \(\omega_i\) are independent identically distributed random variables drawn from the probability distribution \(g(\omega)\). The authors analyze the system in the continuum limit of \(n\to\infty\). They first consider the stability of the phase incoherent state (referred to as “mixing”) which is stable for small \(|K|\), determining values of \(K\) at which it becomes unstable, and what bifurcations occur at these points. Penrose diagrams are used in the analysis. For all-to-all coupling, a unimodal, symmetric bimodal, and asymmetric bimodal distribution \(g(\omega)\) are considered, and pitchfork and Andronov-Hopf bifurcations are found, resulting in various stable partially coherent states. They then consider nonlocal nearest-neighbour coupling, effectively putting the oscillators on a periodic domain. For different distributions \(g(\omega)\), different stable spatiotemporal patterns may now arise. The inclusion of inertia creates several new bifurcation scenarios that do not occur in the Kuramoto model without inertia. The results are illustrated with a number of calculations.