In a large centrifuge used for training astronauts, a small chamber is fixed at

Question

In a large centrifuge used for training 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 2.7 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 2.7 rad/s, the trainee experiences a total acceleration equal to 5.3 times the acceleration due to gravity.
(a)How long is the arm of the centrifuge?
(b)What is the angular acceleration of the centrifuge in the 2nd training exercise?

Explanation / Answer

a) Find the arm L

For the first training exercise: = 2.7 rad/s,

acceleration a1 = 2L = 2.9g,

so L = 2.9g/2 = 3.898 m

b) Find

tangential acceleration at = L

centripetal acceleration ac = 2L = 2.9g

total acceleration a = 4.5 g

a2 = at2 + ac2

at = (a2 - ac2) = 3.44 g = L =3.898 *

= 8.648 rad/s2

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