The disk A rotates about the vertical z-axis with a constant speed $\omega = \dot{\theta} = 0.99$ rad/s. Simultaneously, the hinged arm OB is elevated at the constant rate $\dot{\phi} = 2.07$ rad/s. At time $t = 0$, both $\theta = 0$ and $\phi = 0$. The angle $\theta$ is measured from the fixed reference x-axis. The small sphere P slides out along the rod according to $R = 40 + 236t^2$, where R is in millimeters and t is in seconds. Determine the magnitude of the total acceleration a of P when $t = 0.57$ s.
