Centripetal Circular Motion

[ecsx00]

At its Ames Research Center, NASA uses its large “20-G” centrifuge to test the effects of very large accelerations (“hypergravity”) on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and the astronaut is strapped in at the other end. Suppose that he is aligned along the arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this machine is typically 12.5 g.

1. How fast must the astronaut's head be moving to experience this maximum acceleration?

2. What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?

3. How fast in rpm is the arm turning to produce the maximum sustained acceleration?

Relevant Eqns:
w(omega) = V / R V is the velocity and R is the radius.
a = V^2 / R = w^2 * R

Attempt:
1.
a = w^2 * R
w = sqroot( a / R )
w = sqroot( 123 m/s / 8.84 m ) = 3.73 rad/sec
V = w*R = 3.73 rad/sec * (12.5 * 9.80 m/s^2 ) = 32.9 m/s

I am having trouble with 2. and 3. because I am getting confused with the units and the equations to use. I had problems with 1. and I still don't understand how the answer is correct. Could you guys help me understand the problem? Please don't post answers, just hints or things that will lead me to setting up the problems and getting the answers. Thanks have a nice day!

 

[BruceW]

On question 1), you got the right value for omega. And on the last line, you wrote, v=wR (which is the correct equation). But then you wrote = 3.73 rad/sec * (12.5 * 9.80 m/s^2 ) Which would not have got the right answer. But then at the end, you put 32.9m/s, which is the right answer.

For question 2), its basically asking about the motion of two objects (his head and his feet). So what can you say about their motion which is the same?