Centripetal Acceleration

Question

1: NASA uses large centrifuge to study the effects of large forces on astronauts prior to their going into space. A subject in the 20-G centrifuge, which has a radius of 8.9 m, can have a centripetal acceleration as large as 20.0g, where g equals 9.81 m/s^2 .What is the tangential speed of the subject?

2: Susan runs around a circular track with a circumference of 400 m. If she experiences a centripetal acceleration of 2.79 x 10-2 m/s^2 , how long will it take to run one lap around the track?

3: NASA wants to build a space station that simulates gravity so that the astronauts do not experience as much bone loss while they are in outer space. The space station is designed so that it has a radius of 75.3 m and it rotates counter clockwise. What is the astronaut’s tangential speed when the station is operating properly?

Answer 1

All three problems are to practice the formula

a = v²/r, hence v = √(ar), where

a is the centripetal acceleration,

v is the tangential velocity,

r is the radius of rotation.

1:

a = 20g

r = 8.9 m

v = √(ar) = √(20 × 9.81 × 8.9) = 41.8 m/s

2:

r = 400m/2π

a = 2.79 × 10-2 m/s²

v = √(ar) = √(2.79 × 10-2 × 400/2π) = 1.33 m/s

To run 400 m will take her

400m / 1.33m/s = 300 s = 5 min

3:

r = 75.3 m

a = g

v = √(ar) = √(9.81 × 75.3) = 27.2 m/s

It is possible that you are supposed to answer -27.2 m/s,

where the negative sign indicates counter clockwise rotation.

But I am not really sure why the problem statement explicitly mentions direction of the rotation.