Physics Centripetal Force problem?

[Brij Patel]

1. At what rate a space station 200m in diameter would have to rotate to create gravity equal to 0.7 that at the surface of earth. How fast does it spin, and how long would it take to make a complete rotation? 2. a₂ = v² / 100m
T = 2pi(r) / v

3.
so far: 6.867m/s² = v² / 100m = 26.2 m/s

T = 2pi(100) / 26.2m/s = 24 sec

did I do it right?

 

[TSny]

Welcome to PF!

Your work looks good. The phrase "how fast does it spin" might refer to angular speed rather than linear speed at the outer rim.

 

[Brij Patel]

Welcome to PF!

Your work looks good. The phrase "how fast does it spin" might refer to angular speed rather than linear speed at the outer rim.

The problem is word for word so I assume they're asking for angular speed.
Am I correct, though?

 

[TSny]

If they're asking for angular speed, then you need to calculate the angular speed. I believe your answers for the linear speed and period of rotation are correct.

 

[Brij Patel]

If they're asking for angular speed, then you need to calculate the angular speed. I believe your answers for the linear speed and period of rotation are correct.

w = 2pi / T
w = 2pi / 24 = .2618 rad/sec
is that correct?

 

[Chestermiller]

Yes. It's also v/r = 26.2/100=0.262 rad/sec