# Centripetal Acceleration, etc.

1. Jan 9, 2008

### physicsma1391

[SOLVED] Centripetal Acceleration, etc.

1. The problem statement, all variables and given/known data

A space station is being built for astronauts to begin training for colonizing other planets. The rate of rotation is chosen so that the outer ring (r=2150m) simulates the acceleration of gravity on the surface of Venus (8.62m/s^2).

2. Relevant equations

How long does it take the station to rotate once around its axis (i.e. what is the period?)

What should the radius be of the inner ring so that it smulates the acceleration on the surface of Mercury (3.63m/s^2)

3. The attempt at a solution

I have no idea what to do but perhaps

Fc=ma
ma=m(Vt^2)/r
a=Vt^2/r
Vt=136.1m/s

136.1m/s=2150$$\omega$$
$$\omega$$=.0633rad/s

at=r$$\alpha$$
8.62=2150$$\alpha$$
$$\alpha$$=.004rad/s^2

not sure where to go from here
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 9, 2008

### olgranpappy

you have the correct "omega", now use your formula for the period in terms of omega.

3. Jan 9, 2008

### physicsma1391

what formula is that?

4. Jan 9, 2008

### olgranpappy

Period = 2*pi / omega

that one is certainly in your textbook somewhere

5. Jan 9, 2008

### physicsma1391

hmm.
what are the units on the period? radians?

6. Jan 9, 2008

time...

seconds

7. Jan 9, 2008

### physicsma1391

ohh hahaha ok

8. Jan 9, 2008

### physicsma1391

for the second part of the question, i'm thinking it has to do with omega being the same for both radii?
but how can you find r using accel. and omega?

9. Jan 9, 2008

### olgranpappy

omega is the same for both radii.

so find v for the smaller radius using omega

then you know 'v'. also you know what 'a' must be.

write the formula that relates 'a' to 'v' and 'r' and solve for 'r'.

10. Jan 9, 2008

### physicsma1391

how do i find v for the smaller radius? isnt the equation Vt=r(omega)?

11. Jan 9, 2008

### olgranpappy

yes r*omega

12. Jan 9, 2008

### physicsma1391

but i dont know the radius of the smaller circle

13. Jan 9, 2008

### physicsma1391

i only have omega and the accleration of gravity

14. Jan 9, 2008

### olgranpappy

I know. you are going to solve an equation for 'r'. Write down the equation you are going to solve. the equation for centripital acceleration.

15. Jan 9, 2008

### physicsma1391

a=vt^2/r

16. Jan 9, 2008

### olgranpappy

now substitute in vt in terms of r and omega (post #10)

17. Jan 9, 2008

### olgranpappy

then you'll have an equation for a in terms of r and omega. a is known. omega is known. so solve that equation for r.