The Karin cluster is a young asteroid family thought to have formed only \simeq 5.75 My ago .
The young age can be demonstrated by numerically integrating the orbits of Karin cluster members backward in time and showing the convergence of the perihelion and nodal longitudes ( as well as other orbital elements ) .
Previous work has pointed out that the convergence is not ideal if the backward integration only accounts for the gravitational perturbations from the Solar System planets .
It improves when the thermal radiation force known as the Yarkovsky effect it is accounted for .
This argument can be used to estimate the spin obliquities of the Karin cluster members .
Here we take advantage of the fast growing membership of the Karin cluster and show that the obliquity distribution of diameter D \simeq 1 - 2 km Karin asteroids is bimodal , as expected if the YORP effect acted to move obliquities toward the extreme values ( 0 ^ { \circ } or 180 ^ { \circ } ) .
The measured magnitude of the effect is consistent with the standard YORP model .
The surface thermal conductivity is inferred to be 0.07 -0.2 W m ^ { -1 } K ^ { -1 } ( thermal inertia \simeq 300 - 500 J m ^ { -2 } K ^ { -1 } s ^ { -1 / 2 } ) .
We find that the strength of the YORP effect is roughly \simeq 0.7 of the nominal strength obtained for a collection of random Gaussian spheroids .
These results are consistent with a surface composed of rough , rocky regolith .
The obliquity values predicted here for 480 members of the Karin cluster can be validated by the light-curve inversion method .