Engineers design a cylindrical space habitat that rotates to provide artificial…
PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
Engineers design a cylindrical space habitat that rotates to provide artificial gravity for its occupants. Points on the habitat’s inner surface at a radius of R1=200m from the rotation axis are intended to experience an inward (centripetal) acceleration equal in magnitude to that of Earth’s surface gravity (9.8m/s2).
(1) Part 1: Derive an expression for the linear speed v of a point on the inner surface in terms of its radial distance r from the axis and the common angular speed ω of the habitat.
(2) Part 2: Using the result of part (a), obtain an expression for the centripetal acceleration of a point on the inner surface in terms of r and ω, and hence determine the required angular speed ω that will produce Earth-like gravity at R1.
(3) Part 3: An observation deck is located at a radius of R2=50m. Determine the linear speed and centripetal acceleration experienced by visitors on the deck when the habitat rotates at the angular speed found in part (b).
(4) Part 4: Show algebraically that the ratio of centripetal accelerations at radii R2 and R1 equals the ratio of the radii themselves, and discuss one implication of this result for designing multilevel habitats.