A uniform solid horizontal disk of mass \(M\) and radius \(R\) is mounted on a frictionless vertical axle through its center. The disk is initially rotating freely with a constant angular speed \(\omega_0\). A small robot of mass \(m\) is initially at rest relative to the disk at the center of the disk (\(r = 0\)). At time \(t = 0\), the robot begins to crawl outward along a radial line on the disk. The robot maintains a constant radial speed \(v_0\) relative to the disk. The robot can be treated as a point mass, and its motion is analyzed for the time interval \(0 \le t \le R/v_0\) before it reaches the edge of the disk.