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We studied properties of the strange axial mesons in the relativized quarkmodel. We calculated the $K_1$ decay constant in the quark model and showed howit can be used to extract the $K_1 (^3P_1) - K_1 (^1P_1)$ mixing angle($\theta_K$) from the weak decay $\tau \to K_1 \nu_\tau$. The ratio $BR(\tau\to \nu_\tau K_1 (1270))/BR(\tau\to \nu_\tau K_1(1400))$ is the most sensitivemeasurement and also the most reliable since the largest of the theoreticaluncertainties factor out. However the current bounds extracted from theTPC/Two-Gamma collaboration measurements are rather weak: we typically obtain$-30^o \lesssim \theta_K \lesssim 50^o$ at 68\% C.L. We also calculated thestrong OZI-allowed decays in the pseudoscalar emission model and the flux-tubebreaking model and extracted a $^3P_1 - ^1P_1$ mixing angle of $\theta_K \simeq45^o$. Our analysis also indicates that the heavy quark limit does not give agood description of the strange mesons.Comment: Revised version to be published in Phys. Rev. D. Minor changes. Latex  file uses revtex version 3 and epsfig, 4 postcript figures are attached. The  full postcript version with embedded figures is available at  ftp://ftp.physics.carleton.ca/pub/theory/godfrey/ocipc9512.ps.

Properties of the strange axial mesons in the relativized quark model