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 .

You have been called to testify as an expert witness in a trial involving a head-on collision. car a weighs 1515 lb and was traveling eastward. car b weighs 1125 lb and was traveling westward at 44.0 mph. the cars locked bumpers and slid eastward with their wheels locked for 22.5 ft before stopping. you have measured the coefficient of kinetic friction between the tires and the pavement to be 0.750 . how fast (in miles per hour) was car a traveling just before the collision? (this problem uses english units because they would be used in a u. s. legal proceeding.)

What is the measurement of how fast an object moves relative to a reference point?

Click the game tab at the bottom of the simulation and select level 1. (there is no seesaw balance for this part of the activity.) balance the first equation, and click check to see if you got it right. if you can’t balance it in the first try, you can try again. work through the five equations for level 1. click continue to go on to level 2, and later level 3. each level is more difficult than the one before. keep trying until all the equations are balanced. in one or two sentences, describe how you did in the balancing game. in a few more sentences, explain one strategy you learned for balancing more complex equations.