A high-performance centrifuge used for training astronauts rotates about a vertical axis of rotation. The main arm of the centrifuge rotates, and a test cabin can be moved radially along the arm to adjust the g-force experienced by the pilot, which also changes the system's moment of inertia.
The angular velocity ω\omegaω of the centrifuge arm varies with time ttt over an 8.0 s test run as shown in Figure A.
The total angular displacement of the platform during this entire 8.0 s movement is 5.00 rad5.00\text{ rad}5.00 rad.
Show that ωmax=1.5 rad s−1\omega_{\max} = 1.5\text{ rad s}^{-1}ωmax=1.5 rad s−1.
During the test run, the cabin is moved along the arm, causing the moment of inertia III of the rotating centrifuge about the vertical axis to vary with time ttt. This variation is shown in Figure B.
Show that the torque applied to change the centrifuge's angular velocity reaches its maximum magnitude at t=4.2 st = 4.2\text{ s}t=4.2 s.
Deduce whether the maximum power applied to change the centrifuge's angular velocity occurs at the same time of 4.2 s4.2\text{ s}4.2 s.