Answer parts 1, and 2. Parts 3, 4, 5, and 6 are already answered. While you are
ID: 1787489 • Letter: A
Question
Answer parts 1, and 2. Parts 3, 4, 5, and 6 are already answered.
While you are operating a Rotor (a large, vertical, rotating cylinder found in amusement parks), you spot a passenger in acute distress and decrease the angular velocity of the cylinder from 3.40 rad/s to 2.00 rad/s in 20.0 rev, at constant angular acceleration. (The passenger is obviously more of a"translation person" than a "rotation person.") 1) What is the constant angular acceleration during this decrease in angular speed? 2) How much time did the speed decrease take? 3) [Extra] How much more time would it take until it stop? 4) [Extra] How many more revolutions would it have until it stop? 5) [Extra] Find the linear speed of the rotor 10 seconds before it stop? The radius of the rotation is R = 7.5 m. 6) [Extral Find the magnitude of the centripetal acceleration of the rotor, 10 seconds before it stop.Explanation / Answer
(1) wf^2 - wi^2 = 2 alpha theta
2^2 - 3.40^2 = 2 (alpha) (2 x pi x 20 rad)
alpha = - 0.03 rad/s^2
(2) wf = wi + alpha t
2 = 3.40 - 0.03 t
t =46.7 sec
(3) 0 = 2 - 0.03 t
t = 66.7 sec
(4) 0^2 - 2^2 = 2(-0.03)(2 pi rev)
rev = 10.6 revolutions
(5) w = 0 + (0.03 x 10) = 0.3 rad/s
v = w r = 2.25 m/s
(6) a_r = v^2 / r = 2.25^2 / 7.5 =0.675 m/s^2