How Long Does It Take for a Space Station to Rotate Once?

[physicsma1391]

[SOLVED] Centripetal Acceleration, etc.

Homework Statement

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).

Homework 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)

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

 

[olgranpappy]

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

 

[physicsma1391]

what formula is that?

 

[olgranpappy]

Period = 2*pi / omega

that one is certainly in your textbook somewhere

 

[physicsma1391]

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

 

[olgranpappy]

time...

seconds

 

[physicsma1391]

ohh hahaha ok

 

[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?

 

[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'.

 

[physicsma1391]

how do i find v for the smaller radius? isn't the equation Vt=r(omega)?

 

[olgranpappy]

yes r*omega

 

[physicsma1391]

but i don't know the radius of the smaller circle

 

[physicsma1391]

i only have omega and the acceleration of gravity

 

[olgranpappy]

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

 

[physicsma1391]

a=vt^2/r

 

[olgranpappy]

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

 

[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.