The ability to predict the dynamics of objects, linking applied force to motion, underlies our capacity to perform many of the tasks we carry out on a daily basis. Thus, a fundamental question is how the dynamics of the myriad objects we interact with are organized in memory. Using a custom-built three-dimensional robotic interface that allowed us to simulate objects of varying appearance and weight, we examined how participants learned the weights of sets of objects that they repeatedly lifted. We find strong support for the novel hypothesis that motor memories of object dynamics are organized categorically, in terms of families, based on covariation in their visual and mechanical properties. A striking prediction of this hypothesis, supported by our findings and not predicted by standard associative map models, is that outlier objects with weights that deviate from the family-predicted weight will never be learned despite causing repeated lifting errors.