In a large centrifuge used for training pilots and astronauts, a small chamber i

Question

In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates in a horizontal circle. A trainee riding in the chamber of a centrifuge rotating with a constant angular speed of 2.8 rad/s experiences a centripetal acceleration of 3.1 times the acceleration due to gravity. In a second training exercise, the centrifuge speeds up from rest with a constant angular acceleration. When the centrifuge reaches an angular speed of 2.8 rad/s, the trainee experiences a total acceleration equal to 4.3 times the acceleration due to gravity.

(a) How long is the arm of the centrifuge? m

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

Explanation / Answer

centripetal acceleration , =^2*r =2.5g

so,r=2.5g/2.8^2= 3.13m   <-----answer (a)

total acceleration= 4.8g  = sqrt((tangential acceleration)^2+(centripetal acceleration)^2)

so, tangential acceleration= sqrt((4.8g)^2-(2.5g)^2)=4.1g

so angular acceleration= 4.1g/3.13 =12.84 m/s2    <------answer (b)

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