Centripetal acceleration of rotating cylinders

[mandy9008]

find ω given centripetal acceleration

Homework Statement

It has been suggested that rotating cylinders about 9.0 mi long and 6.4 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

Homework Equations

a_c = Rω²

The Attempt at a Solution

a_c=9.8 m/s²
R= (1/2 (9mi) + 1/2 (6.4mi)) = 7.7mi
9.8 m/s²= 7.7mi ω²
ω = 1.13 rad/s

 

[PhanthomJay]

Homework Statement

It has been suggested that rotating cylinders about 9.0 mi long and 6.4 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

Homework Equations

a_c = Rω²

The Attempt at a Solution

a_c=9.8 m/s²

It's 9.8m/s^2 using SI units, or use 32ft/s^2 if using USA units.

R= (1/2 (9mi) + 1/2 (6.4mi)) = 7.7mi

what does the 9 miles have to do with radius? The radius is 3.2 miles.

9.8 m/s²= 7.7mi ω²
ω = 1.13 rad/s

Ouch. Watch your units. Convert miles to meters if using a=9.8m/s^2, or convert miles to feet if using a =32ft/s^2.