In the film, 2001: A Space Odyssey, astronauts travel through space and experience artificial gravity created by a spinning, cylindrical space station. In order to generate the same gravitational acceleration felt on Earth's surface, a space station rotates so that an astronaut standing inside its outer rim moves tangentially at 42.742.7 m/s. What is the diameter d of the space station?

In the film, 2001: A Space Odyssey, astronauts travel through space and experience artificial gravity created by a spinning, cylindrical space station. In order to generate the same gravitational acceleration felt on Earth's surface, a space station rotates so that an astronaut standing inside its outer rim moves tangentially at 42.742.7 m/s. What is the diameter d of the space station?

Similar questions

A disc with a radius of 53.89 cm is spinning at 40.6 rpm. What is the linear speed (in meters per second) of a point on the rim?
George swings a ball around him, in uniform circular motion. The circle's radius is r. George inadvertently releases the string, and the ball goes outward. He catches the string again, and now the ball goes around him at a new rotation rate, with a new radius r + Δr. Calculate the new rotation rate (in rev/s). r = 2.6 m Δr = 0.5 m Original rotation rate = ωi = 1.6 rev/s The ball's mass is m = 83 grams
A rotating space station is said to create "artificial gravity"-a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. If the space station is 190 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s² at the rim? rpm
It is proposed that future space stations create an artificial gravity by rotating. Suppose a space station in constructed as a 1010.0 m diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. What rotation period (in s) will provide "normal" gravitational acceleration of 9.80 m/s2 at deck level?
a) What is the period of rotation of Venus in seconds? (The period of rotation of Venus in hours is 5,832.5 hr.) Answer in seconds (b)What is the angular velocity (in rad/s) of Venus? (Enter the magnitude.) Answer in rad/s (c) Given that Venus has a radius of 6.1 ✕ 106 m at its equator, what is the linear velocity (in m/s) at Venus's surface? (Enter the magnitude of the linear velocity at the equator.) Answer on m/s
Artificial gravity is a must for any space station if humans are to live there for any extended length of time. Without artificial gravity, human growth is stunted and biological functions break down. An effective way to create artificial gravity is through the use of a rotating enclosed cylinder, as shown in the figure. Humans walk on the inside of the outer edge of the cylinder, which has a diameter of ?=2735 m that is large enough such that its curvature is not readily noticeable to the inhabitants. (The space station in the figure is not drawn to scale.) Once the space station is rotating at the necessary angular speed ? to create an artificial gravity of 1 g, how many minutes would it take the space station to make one revolution?
The International Space Station has a mass of 440,725 kg and is located 420 km away from the surface of the earth. Earth has a mass of 5.97 x 1024 kg and a radius of 6371 km. How quickly does the ISS travel as it orbits the earth, assuming uniform circular motion? Express your answers in rev/day (for angular velocity) and mph (for tangential velocity). Define ALL variables.
George swings a ball around him, in uniform circular motion. The circle's radius is r. George inadvertently releases the string, and the ball goes outward. He catches the string again, and now the ball goes around him at a new rotation rate, with a new radius r + Δr. Calculate the new rotation rate (in rev/s). r = 3.0 m Δr = 1.0 m Original rotation rate = ωi = 1.1 rev/s The ball's mass is m = 160 grams
Now we have a rod-shaped space station of length 1296 m and mass 1.43 x 10^6 kg, which can change its length (kind of like an old-fashioned telescope), without changing its overall mass. Suppose that the station is initially rotating at a constant rate of 1.83 rpm. If the length of the rod is reduced to 1.83 m, what will be the new rotation rate of the space station? 1. 3.01 rpm 6.27 rpm 3 3.76 rpm 4 9.41 rpm
At it's peak, a tornado is 75m in diameter and carries 470m/s wind at its outer edge. What is it's angular speed in radians per second?
The Mars Global Surveyor orbits Mars at an average altitude of 405 km. The average radius of Mars is 3390 km. If it takes the spacecraft 1.95 hours to complete one orbit around the planet, what is it's tangential velocity in kilometers per hour? b) In the activity problem, if the spacecraft's tangential velocity slows down to 10,000 kilometers per hour over a time of 6 minutes, what is the angular acceleration(deceleration) in units of radians per hour squared? Please enter your answer as a positive number with 2 decimal places and no units.gb
Artificial gravity is a must for any space station if humans are to live there for extended length of time. An effective way to create artificial gravity is using a rotating enclosed cylinder. Humans walk on the inside of the outer edge of the cylinder, which has a diameter of D=3450m that is large enough such that its curvature is not readily noticeable to the inhabitants. Once the space station is rotating at the necessary angular speed w to create an artificial gravity of 1g, how many minutes would it take the space station to make one revolution?