Angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is 0.0466 rad/s.
Length of the cylinder, L = 9 mi
= (14.5mi)(1609.344 m / 1 mi)
= 23,335.48 m
Diameter of the cylinder, D = 4.78 mi
= (4.78 mi)(1609.344 m / 1 mi)
= 7692.645 m
Radius of the cylinder, r = D / 2
= ( 7692.645 m) / 2
= 3846.32 m
Centripetal acceleration is given by, ac = v^2 / r
We have the relation between linear velocity (v) and the angular velocity(ω) as
v = r ω
Then, ac = v2 / r
= (rω)2 / r
ac = ω^2 r
If the centripetal acceleration is equals the free fall acceleration of earth, then
ω^2 r = g
ω=0.0466 rad/s
- Angular acceleration is the term used to describe the rate of change in angular velocity. If the angular velocity is constant, the angular acceleration is constant.
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