1. Orbital angularmomentum
Consider the angular wave function:
(see attached)
a) Construct the angular probability density. Show that you can write this as a product of (see attached) and show that both functions are probably normalized.

AngularMomentum. See attached file for full problem description.
A 1.5 kg particle moves in the xy plane with velocity = (4.2i - 3.6j)m/s. What is the angularmomentum of the particle when its position vector is r = 1.5i + 2.2j m

Hello. I am having some trouble with the following PDE:
Laplacian(u(x,y,z)) = u(x,y,z) * (-2*E/h^2)*(1 + (GM/(2(x^2+y^2+z^2)^(1/2))))^4
Where, G,M,E, and h are all constants.
The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-tri

Two lightweight rods L = 19.6cm in length are mounted perpendicular to a vertical axle and at 180 degrees to each other (see figure attached).
At the end of each rod is a m = 640 g mass. The rods are spaced h = 39.6cm apart along the axle. The axle rotates at 28.0rad/s such that the angular velocity vector points upward (+). W

A large turntable rotates about a fixed vertical axis, making one revolution in a time of T. The moment of inertia of the turntable about this axis is I. A child with a mass of m, initially standing at the center of the turntable, runs out along a radius.
What is the angular speed of the turntable when the child is a distance

Suppose a 60kg person stands at the edge of a 6.0m diameter circular platform, which is mounted on frictionless bearings and has a moment of inertia of 1800kgm^2. The platform and runner are initially at rest. Calculate the angular velocity of the platform if the runner begins to run 4.2m/s.

Consider a deuterium atom (composed of a nucleus of spin I = 1 and an electron). The electronic angularmomentum is J = L + S, where L is the orbital angularmomentum of the electron and S is its spin. The total angularmomentum of the atom is F = J + I, where I is the nuclear spin. The eigenvalues of J^2 and F^2 are J(J+I)h^2

See attachment please.
Need FBD for each case.
The 0.2 kg ball ( ball is sliding not rotating) and the supporting cord are revolving about the vertical axis on the fixed smooth conical surface with an angular velocity of W = 4 radians/sec. The green ball is held in position b = .3 m by the tension T in the yellow cord.
If b