Question

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

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.