Question

Astronauts are trained for take-off in a high-speed centrifuge of 4.7 m radius that spins in the horizontal plane.

(a) What is the average angular speed required for the astronauts to train at 3.5 g's?
(b) How fast (linear speed) are they moving at that time?
(c) What is the direction of the astronaut's apparent weight?

Answer 1

Answer:

a) $1.94 \frac{rad}{s}$

b) $9.12\frac{m}{s}$

c) Towards the center of the centrifuge

Explanation:

a)

Becuse the centrifuge rotates in circular motion, there's an angular acceleration tha simulates high gravity accelerations

$a_{rad}=\omega r^{2}$

with r the radius and ω the amgular velocity, in or case $a_rad=3.5g$ so:

$3.5g=\omega r^{2}$ and g=9.8$\frac{m}{s^{2}}$

solving for ω:

$\omega=\frac{3.5g}{r^2}=\frac{3.5*9.8}{4.2^2}$

$\omega = 1.94 \frac{rad}{s}$

b) Linear speed (v) and angular speed are related by:

$v=\omega r =(1.94)(4.7)$

$v= 9.12\frac{m}{s}$

c) The apparent weigth is pointing towards the center of the circle, becuse angular acceleration is pointing in that direction.