Problem 5.199

Experience shows that a body irradiated with light with circular polarization acquires a torque. This happens because such a light possesses an angular momentum whose flow density in vacuum is equal to \(M=I / \omega,\) where \(I\) is the intensity of light, \(\omega\) is the angular oscillation frequency. Suppose light with circular polarization and wavelength \(\lambda=0.70 \mu \mathrm{m}\) falls normally on a uniform black disc of mass \(m=10 \mathrm{mg}\) which can freely rotate about its axis. How soon will its angular velocity become equal to \(\omega_{0}=\) \(=1.0\) rad/s provided \(I=10^{\circ} \mathrm{W} / \mathrm{cm}^{2} ?\)