In a 'Rotor' amusement park ride, riders stand against the inner wall of a rotating vertical cylinder. Once the cylinder reaches a certain speed, the floor drops away. If the cylinder rotates at a constant angular speed of 2 rad/s and the coefficient of static friction between a rider's clothing and the wall is 0.5 , what is the minimum radius of the cylinder required to prevent the riders from sliding down? (Take g

Step-by-step solution

The normal force N exerted by the wall on the rider provides the necessary centripetal force: N = m ^2 R For the rider not to slide down, the upward static friction f must balance the downward gravitational force mg . The maximum available static friction is N . Therefore, the condition to prevent sliding is: mg N mg (m ^2 R) The mass m cancels out from both sides: g ^2 R Rearranging for the radius R : R g ^2 Substitute the given values g = 10 m/s ^2 , = 0.5 , and = 2 rad/s: R 10 0.5 (2)^2 R 10 0.5 4 R 10 2 R 5 m T