Sometimes, you observe one object, and instead of getting one thermal spectrum, you get two! Below is a spectrum taken of a nearby star. Looking at the spectrum, you should see two clear thermal peaks. The one on the left, peaking in the visible range, is from the star. What's causing the other peak?

It turns out that this peak is being produced by a debris disk surrounding this very young star. Debris disks are commonly seen around young stars - they are usually present during planet formation and then eventually dissipate. What temperature is the material in this disk at? Show your work and explain your reasoning clearly.

Hint: Pay attention to the wavelength units!!

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.