A centrifuge is often used for astronaut training. A simplified version is sketched in the figure below, in which a cockpit is rigidly attached to an arm, which is driven by a motor and rotates in the horizontal plane (shown from above). In a particular test, starting from rest, the driving motor supplies a constant angular acceleration of 0.5 rad/s2 , and the distance from the astronaut to the rotation axis is 10 m. Find the acceleration of the astronaut (with respect to the ground) as a function of time. The reference frames are as follows: OXYZ is fixed to the ground, and Oxyz is fixed to the arm.

10 m Cockpit X 0.5 rad/s2