While ideal rotational surfaces of the pivot and the race of ball bearings can touch the spherical ball surfaces only at mathematical points, these surfaces actually “flatten” at the contact, due to elastic compression so that contact occurs over a finite area. It is shown in this paper that as a result of this flattening, owing to unavoidable small relative slipping over some of the contact areas, even the most precise and flawless ball bearings possess definite friction. This source of unavoidable friction is analyzed, and the frictional torque due to it is computed for an individual ball, for the whole bearing, and for both bearings holding a rotor or gimbal.
Native American consultation and collaboration have become integral parts of national forest management, but the number of applicable laws, regulations, rules, and policies can make this process a daunting one. Over the years, a series of programmatic agreements (PAs) have been developed by the Ozark-St. Francis and Ouachita National Forests (OSFONF) to help with heritage resource management. These PAs have been continuously revised and improved, culminating in a document developed with the cooperation of more than a dozen tribes, state agencies, and the federal Advisory Council on Historic Preservation. Important lessons for managers can be gleaned from the 2006 OSFONF PA and related consultations. For example, in addition to providing a collaborative framework that streamlines OSFONF management, the PA facilitates other actions by identifying undertakings exempted from the National Historic Preservation Act of 1966 (NHPA) compliance process. Beyond their operational utility, PAs can build trust and enduring relationships with tribal stakeholders, both of which are vital to further collaboration. Improved relationships benefit participants with expanded training opportunities and logistical support for shared understandings of patrimonial areas and traditional ecological knowledge. PAs can also serve as models for nonfederal landowners, helping them meet forest sustainability requirements and reach out to Native Americans with ancestral ties to the land.
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