OK, so I just want to show ω = E/h = kv, but I keep running into errors, I don't know why.
So, let's start with momentum:
p^2 / 2m = E
p^2 = 2mE
p = sqrt(2mE)
h/λ = sqrt(2mE)
hk = sqrt(2mE)
k = sqrt(2mE)/h
So far so good. Now let's start with conserved Energy
E= ½ mv^2
2E/m = v^2
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The Attempt at a Solution
My problem is not finding the Lagrangian. But finding the kinetic energy! The translational kinetic energy would obviously be the following:
4 persons each with mass m stand out on the edge of the carousel that rotates with angular velocity W0. carousel has mass 4m, radius r and inertia I = 2mr^2. The 4 persons then go all the way to the center of the carousel.
Show that the final angular velocity W1 = 3W0