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(Solved): Question #4. The Rotor The rotor a device found at amusement parks. It is a large hollow cylinder o ...
Question #4. The Rotor The rotor a device found at amusement parks. It is a large hollow cylinder of radius \( R \) with canvas walls. Riders enter from a side door and place themselves against the wall. The cylinder is gradually spun to a peak angular speed, at which time the floor falls away, leaving the riders stuck to the walls. Sometime later the rotor slows down, the floor reappears and the passengers stagger out. (a) Draw the FBD of a rider pinned to the wall. Label all the forces on the rider. (b) At the peak value angular speed, the cylinder rotates at constant speed. Obtain an equation for the period \( T \) of the motion in terms of \( R, v, g \), and \( \mu_{s} \) (c) For a radius \( R=2.5 \mathrm{~m} \), and a coefficient of static friction between clothing and the canvas walls \( \mu_{s}=0.40 \), what is the minimum speed for the cylinder to prevent the riders from falling down the walls? Note the result is independent of rider mass. (d) Use your result in (c) and calculate the corresponding angular speed in revolutions per minute (rpm). (e) For a rider of \( 45 \mathrm{~kg} \) mass, calculate the magnitude of the centripetal force the rider endures during at the peak rotation rate.