Design Space Station Homework: Rotation Speed & Gravitational Acceleration

[PrideofPhilly]

Homework Statement

Part 1:

You want to design a large, permanent space station so that no artificial gravity is necessary. You decide to shape it like a large coffee can of radius 322 m and rotate it about its central axis. The acceleration of gravity is 9.8 m/s2. What rotation speed would be required to simulate gravity?

Part 2:

If an astronaut jogged in the direction of the rotation at 5 m/s, what is the simulated gravitational acceleration the astronaut would feel?

Homework Equations

a = v^2/r

ω = v/r

a = vω

The Attempt at a Solution

For Part 1:
9.8 = v^2/322 m
v^2 = 3155.6
v = 56.17472741 m/s

vω = v^2/r
ω = v/r
ω = (56.17472741 m/s)/(322 m)
ω = 0.174456 rad/s


For Part 2:

v = rω

I don't really know where to begin for this part.

 

[LowlyPion]

a = v²/r = ω²r = g

ω = (g/r)^1/2

... which yields your answer.

In part 2 they want you to determine what happens when Kier Dullea (astronaut from 2001:Space Odyssey) is jogging, thereby increasing his speed (and the g force) by 5 m/s in the direction of rotation.

 

[PrideofPhilly]

Oh...okay, so:

astronaut's speed: 56.17472741 m/s + 5 m/s

a = v^2/r
a = (61.17472741 m/s)^2/322 m = 11.62223624 m/s^2

 

[LowlyPion]

Oh...okay, so:

astronaut's speed: 56.17472741 m/s + 5 m/s

a = v^2/r
a = (61.17472741 m/s)^2/322 m = 11.62223624 m/s^2

Pretty much.

Since 9.8 is the given precision of gravity, maybe the correct form of your answer would be 11.6, depending on your instructor.