FYKOS Year 28 Series 6 Problem 3 — The Interview · FYKOS 28 #28.6.3

Physics · mechanics

Problem

One of the offices of lord Vetinari has a circular layout with a perimeter

R

and is placed on bearings, thanks to which it can turn around its axis. To ensure maximum rotation it uses an engine that can apply any moment of force. During the turning the room has a torque of friction acting on it

M_{0}

, independent of speed, which is equivalent to the static friction torque. The chair for visitors is positioned so that a person will feel the rotation only if it will exceed

ε_{0}

. Determine what is the smallest time it will take to turn by 180°, so thatthe visitor won't notice and what is the work required to achieve it. The mass of the room, that can be approximated to a homogeneous disc, is

m

. Bonus: Assume that the visitor will feel the roation only if the change in angular acceleration is greater than

j_{0}

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