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 .

because it says use -2,0,and 2 for x, we can plug those numbers into the equation. y/4=3/4(-2)+2   y/4= -1 1/2 +2 now to get x by itself, we can multiply each side by 4. y=-6+8 which equals y=2 when x=-2. now you can do the same thing with 0 and 2 as x. you get y=8 when x=0 and y=14 when x=2.

x   |   y

-2 |   2

0   |   8

2   |   14

c) up is the direction the magnetic force is acting on the charge.

-4 on

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)