Accelerating too much can cause someone to pass out. Astronauts go through training to build up their ability to stay conscious during periods of large acceleration. Normal humans without training black out when exposed to prolonged accelerations of over 5 g (five times the acceleration due to gravity).
A large spinning ride was designed to expose astronauts to high levels of centripetal acceleration. If the "ride" has a radius of 12.0 m, what angular velocity is needed to subject an astronaut to 9.00 g?
To find the angular velocity needed to subject an astronaut to 9.00 g of centripetal acceleration, we can use the formula for centripetal acceleration:
a = r * ω^2
Where:
a = centripetal acceleration (9.00 g = 9.00 * 9.81 m/s^2)
r = radius of the ride (12.0 m)
ω = angular velocity
Plugging in the values, we get:
9.00 * 9.81 = 12.0 * ω^2
88.29 = 12.0 * ω^2
ω^2 = 88.29 / 12.0
ω^2 = 7.3575
ω = √7.3575
ω ≈ 2.71 rad/s
Therefore, an angular velocity of approximately 2.71 rad/s is needed to subject an astronaut to 9.00 g of centripetal acceleration on the spinning ride with a radius of 12.0 m.