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 2.4 rad/s experiences a centripetalacceleration of 3.1 times theacceleration due to gravity. In a second training exercise, thecentrifuge speeds up from rest with a constant angularacceleration. When the centrifuge reaches an angular speedof 2.4 rad/s, the traineeexperiences a total acceleration equal to 4.6 times the acceleration due to gravity. (a) How long is the arm of the centrifuge? (in m)


(b) What is the angular acceleration (magnitude) of the centrifugein the second training exercise? (in rad/s2) (a) How long is the arm of the centrifuge? (in m)


(b) What is the angular acceleration (magnitude) of the centrifugein the second training exercise? (in rad/s2)

Explanation / Answer

centripetal acceleration = Ac = 2r = 2.4*2.4*r = 3.1*9.8 m/s2 => r = length of arm of centrifuge = 5.274m Let the angular acceleration have aa magnitude . So, = t       A = [Ac2 +(r)2]      Now, Ac = 2r      So, r = [A2 -Ac2] = g*[(4.6)2 - (3.1)2]= 3.4*g = 33.31 m/s2      => = 6.315 rad/s2

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