Centripetal Acceleration/Gravity Problem

[Drokro0707]

Homework Statement

A circular "space hotel" in orbit around the Earth has a diameter of 355m. In order to produce "fake gravity" along the outer rim, it is desired to rotate it at a speed that will produce a centripetal acceleration of 9.81m/s^2. Note the geometry: people walking on the inside of the outer rim will weigh the same as if they were on Earth. Drawing will help.

a)Find the tangential speed of a point on the rim when the station is producing the required centripetal acceleration.

b)Find the stations angular velocity under those conditions, in radians per second.

c)If you're "below deck" at a point 77m from the outer rim, how much "gravity" will you experience?

d)If you start moving from the rim toward the central hub of the space station, what will it feel like? How will perception change as you move?

Homework Equations

v=at
a=dv/dt
ac=v^2/r=rω^2
ω=ø/t

The Attempt at a Solution

Im assuming that the centripetal acceleration formula would be used to solve for part a and then the angular velocity formula would help solve part b. For part c since gravity is mentioned I don't know what to do exactly but I think that's where the 9.81m/s^2 would come into play. As for part d, I have not the slightest clue.

 

[Andrew Mason]

Homework Statement

A circular "space hotel" in orbit around the Earth has a diameter of 355m. In order to produce "fake gravity" along the outer rim, it is desired to rotate it at a speed that will produce a centripetal acceleration of 9.81m/s^2. Note the geometry: people walking on the inside of the outer rim will weigh the same as if they were on Earth. Drawing will help.

a)Find the tangential speed of a point on the rim when the station is producing the required centripetal acceleration.

b)Find the stations angular velocity under those conditions, in radians per second.

c)If you're "below deck" at a point 77m from the outer rim, how much "gravity" will you experience?

d)If you start moving from the rim toward the central hub of the space station, what will it feel like? How will perception change as you move?

Homework Equations

v=at
a=dv/dt
ac=v^2/r=rω^2
ω=ø/t

The Attempt at a Solution

Im assuming that the centripetal acceleration formula would be used to solve for part a and then the angular velocity formula would help solve part b. For part c since gravity is mentioned I don't know what to do exactly but I think that's where the 9.81m/s^2 would come into play. As for part d, I have not the slightest clue.

You have the right formula for a_c. Use ω = dø/dt = Δø/Δt (ω being constant).

At what value of ω does the centripetal acceleration = the acceleration due to gravity on the Earth surface?

d) is a little tricky to analyse. Do an experiment: spin a playground merry-go-round, jump on the outside and then move toward the centre. Will the centripetal force change? How? What will happen to your tangential speed? What effect will that change have?

AM