explain A space station ls oonstructed in the shape of a hollow ring of mass s.o

Question

explain

A space station ls oonstructed in the shape of a hollow ring of mass s.os × 1a" kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius 135 m. At rest when constructod, the ring is set rotating about its axis so that the people inside exparience an effective free-fall acceleration oqual to g. (See figura belaw.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring. (a) What angular momentum does the space station acquire? kg·m"/s (b) For what time interval must the rockets be firad if each exerts a thrust of 130 N? Need Help? Headi

Explanation / Answer

part A : formula for centripetal acceleration a = v^2/r or rW^2

rearranging for angular velocity W =sqrt[g/r]

Moment of inertia of a ring, I=mr2

angular momentum, L=I*W=mr2*[sqrt[g/r]

so L=mr*sqrt[gr]

L =(5.05*10^4)(135)*sqrt[9.8*135]

L= 2.47*10^8 Kg m/s

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part B : Torque on the station is given T=2*r*F = I*alpha

T =mr^2*alpha

Angular acclration A = alpha=2F/mr

use the kinematic equation for angular velocity W=Wo+alpha*t

W =0+alpha*t

t =W/alpha

t =sqrt[g/r]*(mr/2F)

t =(0.5* m/F)sqrt(gr)

t =0.5* (5.05*10^4/130)* sqrt(9.8*135)

t =

t=7064 seconds or 1.96 hour

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