We present the problem of relativistic torques with particular reference to the right-angle lever problem and outline a simple solution. The important elements of our solution are, first, a reexamination of the classical relation between torque and angular momentum and, second, the consequent realization that in relativistic analysis there exists a net internal torque which exactly cancels the net external torque experienced by an extended body in dynamic equilibrium. We find that the lever has constant angular momentum according to all Lorentz inertial reference systems and that this is consistent with the relativistic relationship between torque and angular momentum. Our solution is not restricted to relativity. It is valid for a wider class of theoretical frameworks.

The Trinity River below the navigation lock and salinity control structure at Wallisville, TX, has experienced significant shoaling in recent years. The location of the shoal is immediately downstream of the confluence with the Old River Cut Off channel (ORCO), which has been enlarging and progressively carrying a greater fraction of the discharge at the expense of the Trinity River. The reduction in flow in the Trinity River below the ORCO has resulted in reduced sediment transport capacity which created the shoaling problem. This report presents the results of a numerical model study to evaluate alternatives for potential mitigation of the shoaling problem. The alternatives include dredging the shoal and placing the material into the ORCO, damming the ORCO, and creating partial closure of the ORCO. The model results illustrate the basic problem of an elongated navigation channel with numerous distributary pathways for water and sediment within a deltaic system. The routing of all flow down the Trinity River will result in erosion of the current shoal, but shoaling will then occur below the next bayou that extracts flow from the river. DISCLAIMER: The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. All product names and trademarks cited are the property of their respective owners. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.

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