Construct the classical Hamiltonian for a single particle from the corresponding Lagrangian in Cartesian, cylindrical, and spherical coordinates. Identify the canonical momenta required in each case to show that € H = 1 2m (px 2 + py 2 + pz 2 )+V(x, y, z) H = 1 2m ( prho 2 + pφ 2 rho2 + pz 2 )+V(rho,φ,z) H = 1 2m ( pr 2 + pθ 2 r 2 + pφ 2 r 2 sin2 θ )+V(r,θ,φ).

You are traveling in a car going at a constant speed of 100km/h down a long, straight highway. you pass another car going in the same direction which is traveling at a constant speed of 80km/h. as measured from your car's reference frame this other car is traveling at −20km/h. what is the acceleration of your car as measured from the other car's reference frame? what is the acceleration of the other car as measured from your car's reference frame?

Waves that cause the most damage during an earthquake are a. surface waves c. s waves b. p waves d. ocean waves

What are atoms of the same element with varying number of neutrons