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 2.3 rad/s experiences a centripetal acceleration of3.5 times the acceleration due to gravity.In a second training exercise, the centrifuge speeds up from restwith a constant angular acceleration. When the centrifuge reachesan angular speed of 2.3 rad/s, the traineeexperiences a total acceleration equal to 5.3 times the acceleration due to gravity. (a) How long is the arm of the centrifuge?
1 m

(b) What is the angular acceleration (magnitude) of the centrifugein the second training exercise?
2rad/s2 (a) How long is the arm of the centrifuge?
1 m

(b) What is the angular acceleration (magnitude) of the centrifugein the second training exercise?
2rad/s2

Explanation / Answer

So, from the first exercise we can say: the centripital acceleration is: a = ^2 * R 3.5/(2.3^2) = R that gets you 1. for 2, you know that the centripetal acceleration is 3.5 because is 2.3 rad/s. So,the total acceleration is: a(total) = *R + a(centripetal) (5.3*g)^2 = ( * R)^2 +(3.5)^2                g = 9.81 m/s^2 = ((5.3*g)^2 - (3.5)^2)/ R where you solved for R in part 1.

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