Find the temperature increase of a rotating disk

[Edward258]

Homework Statement

It's a Blackbody radiation problem:
A beam of wavelength λ, in the state of right circular polarization, leads to an absorbent disk.The mass of the disk is m, it's specific heat is C, and its moment of inertia is I .The disk is initially at rest, but after a lapse of time has an angular velocity Ω. Show that the temperature increases in:

ΔT=(IΩ/mC)(2πc/λ-Ω/2)

Homework Equations

Q=CmΔT

The Attempt at a Solution

From the equation;
Q=CmΔT
I can get ΔT
ΔT=Q/Cm
And
Q=U2-U1
So
ΔT=(U2-U1)/Cm
But I don't know how to justify that;
U1=IΩ²/2 ------- Rotational kinetic energy
U2=(IΩ2πc)/λ --------- con E=hc/λ Photon energy

 

[DrClaude]

Any good reference on classical mechanics should tell you the relation between angular velocity and rotational kinetic energy. Otherwise, you need to use the fact that each circularly polarized photon has an angular momentum of ħ.