Question

A 70.0 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 10.0 m) & spun at a constant angular velocity of 16.3 rpm.
a. What is the angular velocity of the centrifuge in rad/s?
b. What is the linear velocity of the astronaut at the outer edge of the centrifuge?
c. What is the centripetal acceleration of the astronaut at the end of the centrifuge?
d. How many g’s does the astronaut experience?
e. What is the centripetal force & net torque experienced by the astronaut? Give magnitudes & directions.(Please show the formulas/wor

Answer 1

a. one rotation is equal to \[2\pi rad\] so you will convert 16.3 rpm to rps and then multiply by \[2\pi \]

Answer 2

b. linear velocity is equal to \[v = \omega r\] so solve a and plug in your angular velocity and multiply by the radius of the centrifuge.

Answer 3

c. centripetal acceleration is equal to \[a _{c}=\omega ^{2}r\] so solve b and multiply by angular velocity.

Answer 4

d. to calculate the g force I think you need to take \[\frac{ a _{c} }{ 9.8 }\] but I'm not entirely sure on this.

Answer 5

e. the centripetal force would be \[F _{c}=\frac{ mv ^{2} }{ r }\]
and the net torgue is \[\tau = F _{c} r\] The direction for torque would be along the z axis

Answer 6

If the angular velocity is constant, there is no net torque.