Show that if the potential in the Lagrangian contains velocity-dependent terms, the canonical momentum corresponding to a coordinate of rotation θ of the entire system is no longer the mechanical angular momentum Lθ but is given by pθ = Lθ − i n ? ri 3∇viU, where ∇v is the gradient operator in which the derivatives are with respect to the velocity components and n is a unit vector in the direction of rotation. If the forces are electromagnetic in character, the canonical momentum is therefore pθ = Lθ + i n ? ri 3 qi c Ai .

8. why do radio telescopes convert radio waves (analog signals) to electrical (digital) signals for analysis? (hint: what did the article say about the advantages of digital signals? )

Which are advantages of renewable resources? check all that apply. renewable energy supplies are completely reliable everywhere. some renewable resources will never be used up. little or no waste is produced by renewable resource plants. electricity can be generated in large quantities. many renewable energy facilities have lower operating costs.

Isobars are lines of constant or equal pressure on a weather map. they can be used to find areas of low or high pressure over a broad area, and they can tell us how intense the system may be. on weather maps, you may have noticed areas that have a large l or h over a region with lines circling around them. the l stands for low pressure and h stands for high pressure. the lines circling them are isobars. check out the pressure system and isobars over georgia and florida. what is the present weather in this area ? a) clear and sunny b) cold and cloudy c) changing weather d) lots of precipitation