In a large centrifuge used for training pilots and astronauts, asmall chamber is

Question

In a large centrifuge used for training pilots and astronauts, asmall chamber is fixed at the end of a rigid arm that rotates in ahorizontal circle. A trainee riding in the chamber of a centrifugerotating with a constant angular speed of 3.0 rad/s experiences acentripetal acceleration of 2.8 times the acceleration due togravity. In a second training exercise, the centrifuge speeds upfrom rest with a constant angular acceleration. When the centrifugereaches an angular speed of 3.0 rad/s, the trainee experiences atotal acceleration equal to 4.8 times the acceleration due togravity. (a) How long is the arm of thecentrifuge? (b) What is the angular accelerationin the second training exercise?

Explanation / Answer

centripetal acceleration = Ac = 2r = 2.2*2.2*r = 3.2*9.8 m/s2 => r = length of arm of centrifuge = 6.479m Let the angular acceleration have aa magnitude . So, = t       A = [Ac2 +(r)2]      Now, Ac = 2r      So, r = [A2 -Ac2] = g*[(4.5)2 - (3.2)2]= 3.163*g = 31.03 m/s2      => = 4.79 rad/s2

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