Angular speed after a robot arm retracts a mass (conservation of angular momentum)

A robot arm holding a small payload spins freely about a fixed vertical axis with no external torque. Model it as a point mass $m = 2\ \text{kg}$ at radius $r_1 = 0.5\ \text{m}$ rotating at angular speed $\omega_1 = 4\ \text{rad/s}$. The arm retracts the payload radially inward to $r_2 = 0.2\ \text{m}$. Neglect the arm's own inertia. What is the new angular speed $\omega_2$ in rad/s?