Centripetal Acceleration or Circular motion?

Hey guys im stuck on this problem:

Answer 1

b) the astronaut’s feet are 6.84m from the rotation axis, if the head is moving at 33m/s, the feet are moving at a speed of 33m/s x (6.84m/8.84) = 25.5m/s

the centrip accel at this distance at this speed is

a=v^2/r = (25.5m/s)^2/6.84m = 95.32m/s/s

if the accel at the head is 12.5 x 9.81m/s/s = 122.6m/s/s, the difference is 27.3m/s/s

3. 1 full rev executes a distance of 2 pi x 8.84m = 55.5m

if the speed is 33m/s, then it takes 55.5m/33m/s = 1.68 s for one rev; therefore, there will be

60s/min / 1.68s/rev = 35.7rev/min

Answer 2

Let w be the be the angular velocity of the arm in rad/s and v velocity of head in m/s.
1. a = (v^2)/(8.85) = 12.5*9.81 or v = sq rt[12.5*9.81 *8.85] = 32.94 0r 33.0 m/s = (w^2)*8.85; or w^2 = 3.72 (rad/s)^2

2. w = (v/r) is same for both head and legs and also a = (w^2)*r = 3.72*(8.85-2.00) = 25.498 or
25.5 m/s^2 or 2.599*g or 2.6*g

3. w^2 = 3.72 or w = 1.929 rad/s = {1.929/(2*pi)}*60 rpm = 18.42 or 18.4 rpm

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