What Is the Fake Gravity on a Circular Space Hotel Orbiting Earth?

[anthonyslvtr]

Homework Statement

A circular space hotel in orbit around the Earth has a radius of 220m. in order to produce "fake gravity" along the outer rim, it is desired to rotate at a speed that will produce a centripetal acceleration of 9.81 m/s^2.
A) find the tangential speed of appoint on the rim when the station is producing the required centripetal acceleration.
B) Find the station's 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 your perception change as you move?

Homework Equations

v^t = √(a_c*r)
ῳ = v/r

The Attempt at a Solution

A) I interpreted the following: a_c = 9.81m/s^2 and r= 220m. With these I plugged into the first equation to find the tangential velocity which came out to be v_t=46.456m/s.

B) To find the angular velocity I plugged in the v_t and r in the second relevant equation and found ῳ=0.211rad/s.

C) Assuming I did the first two parts correctly (let me know if I did not please), this is what's giving me a problem. If 77 m "below deck" that would give you a new radius of 143m. I believe this would change your a_c or completely eliminate it. Would the following equation work: a_c = rῳ²?
I'm open to discuss this back and forth rather than just asking for help or an answer.

 

[Svein]

Would the following equation work: ac = rῳ2?

Yes.