Rotation period of a space station

In summary: T ) ² ) / rNow use the quadratic equation:T=4*a*r^2In summary, for a centrifuge with a diameter of 13.5 meters, the rotation period needed to produce a 2 g centripetal acceleration is 8.13 seconds.
  • #1
ross moldvoer
16
0

Homework Statement


To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of
If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 2 g? of 5g?

Homework Equations


T=2*pi*r/v

The Attempt at a Solution


i tried solving for v using a=v^2/r and then plugging it in but i got the wrong answer
 
Physics news on Phys.org
  • #2
ross moldvoer said:

Homework Statement


To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of
If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 2 g? of 5g?

Homework Equations


T=2*pi*r/v

The Attempt at a Solution


i tried solving for v using a=v^2/r and then plugging it in but i got the wrong answer
Please post your working, or we can't tell if or where you went wrong.
(Are you sure it asks for a centripetal acceleration of that magnitude, not a net g-force corresponding to it?)
 
  • #3
i did 9.8=v^2/6.75, v^2=(9.8)(6.75)=66.15 v=8.13
then i plugged v into the equation i gave above
 
  • #4
ross moldvoer said:
i did 9.8=v^2/6.75, v^2=(9.8)(6.75)=66.15 v=8.13
then i plugged v into the equation i gave above
It says 2g and 5g, not 1g.
 
  • #5
You need to introduce T into the root equation.
You have a = v ² / r
But v = ( 2 * π * r ) / T
 
  • #6
then what equation should i use to solve for v since i don't know T?
 
  • #7
ross moldvoer said:
then what equation should i use to solve for v since i don't know T?
I think dean barry is suggesting you eliminate v between the two equations so that you can go straight to finding T without having to calculate v. That's good advice generally, since it serves to reduce accumulation of rounding errors, but I don't think it matters here.
Do you have a response to my post #4?
 
  • #8
i did accidently forget to do 2g instead of just 9.8.
 
  • #9
ross moldvoer said:
i did accidently forget to do 2g instead of just 9.8.
So does that resolve your issue, or do you still have the wrong answer?
 
  • #10
that fixed it. thanks a ton
 
  • #11
so after solving for omega i plug it into T=2*pi*r/v? i get 407 when i do this and this seeems a little high
 
  • #12
ross moldvoer said:
so after solving for omega i plug it into T=2*pi*r/v? i get 407 when i do this and this seeems a little high
Yes, that's way too high. Please post all your steps.
 
  • #13
Take: a = v ² / r
You know:
v = ( 2 * π * r ) / T
( which introduces T into the game )
You get: a = ( ( 2 * π * r ) / T ) ² ) / r
Transpose for T
 

FAQ: Rotation period of a space station

What is the rotation period of a space station?

The rotation period of a space station is the time it takes for the station to complete one full rotation on its axis. This can vary depending on the design and size of the station, but most space stations have a rotation period of about 90 minutes.

Why is the rotation period of a space station important?

The rotation period of a space station is important for several reasons. It helps to create artificial gravity, which is necessary for the health and well-being of astronauts on long-term missions. It also helps to evenly distribute sunlight and heat throughout the station, and allows for easier docking and maneuvering of spacecraft.

How is the rotation period of a space station determined?

The rotation period of a space station is typically determined during the design and construction phase. Engineers use mathematical calculations and computer simulations to determine the optimal rotation period for the specific needs of the station. Once the station is in orbit, the rotation period can be measured and adjusted if necessary.

Can the rotation period of a space station be changed?

Yes, the rotation period of a space station can be changed. This can be done by adjusting the speed of the station's rotation or by changing the orientation of the station's axis. However, changing the rotation period can be a complicated and delicate process, and is typically only done if necessary.

What are the potential effects of a longer or shorter rotation period on a space station?

A longer or shorter rotation period can have various effects on a space station. A longer rotation period may result in reduced artificial gravity, while a shorter rotation period may cause astronauts to experience motion sickness. It can also affect the distribution of sunlight and heat, and the maneuverability of spacecraft. Therefore, it is important for the rotation period to be carefully considered and maintained for the well-being and functionality of the space station.

Similar threads

Problem 9.2 Classical Mechanics: Astronaut in a rotating space station
Replies
1
Views
3K
Acceleration in uniform circular motion is uniform or non-uniform?
2
Replies
55
Views
2K
What is the Height of the International Space Station Above the Earth's Surface?
Replies
2
Views
3K
Centripetal Force / circular motion question
Replies
7
Views
3K
Calculating Rotations for a Space Station
Replies
1
Views
2K
How Long Should Rockets Fire to Rotate a Space Station?
Replies
4
Views
2K
How Do You Calculate Centripetal Acceleration in a Blood Centrifuge?
Replies
8
Views
1K
Calculating Angle & Speed to Reach Planet's Moon from Station Orbit
Replies
1
Views
1K
Conservation of Angular Momentum and Energy in a Rotating Space Station
Replies
1
Views
1K
Centrifugal acceleration in rotating frame
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top