The electromagnetic field is invariant under a gauge transformation of the scalar and vector potential given by a rightarrow a + psi (r, t), phi rightarrow phi - l / c psi / t, where psi is arbitrary (but differentiable). what effect does this gauge transformation have on the lagrangian of a particle moving in the electromagnetic field? is the motion affected?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

Aphysical change is a change in the size, shape,, or stafe of matter true or false

How to tell if two objects are in thermal equilibrium 1.the objects have the same temperature 2.the objects are the same size 3.the objects are touching each other 4.the objects temperatures are changing