A cylindrically shaped space station is rotating about the axis of the cylinder

Question

A cylindrically shaped space station is rotating about the axis of the cylinder to create artificial gravity. The radius of the cylinder is 79.0 m. The moment of inertia of the station without people is 2.94 109 kg · m2. Suppose that 505 people, with an average mass of 65.8 kg each, live on this station. As they move radially from the outer surface of the cylinder toward the axis, the angular speed of the station changes. What is the maximum possible percentage change in the station's angular speed due to the radial movement of the people?
%

Explanation / Answer

Given that the radius of cylinder is r = 79 m Moment of inertia is I = 2.94*109 kg.m2 Number of people are N =505 mass of each person is m = 65.8kg ------------------------------------------------------------------------- Since there is no external torque on the systemso angular momentum conserved Iinitial*?1 =Ifinal*?2 ( I + Ipeople)*?1 = I*?2 ( I +N*m*r2)*?1 = I*?2 ?2 = ( I + N*m*r2)*?1 / I = ( 1 + N*m*r2 / I)*?1 the change is ( ?2- ?1 ) = ( 1 + N*m*r2 / I )*?1 -?1 = N*m*r2*?1 / I The ration is (?2 - ?1) /? = N*m*r2 / I ?? / ? = N*m*r2 / I =(505)(65.8 kg)(79.0 m)^2/(2.94 x10^9 kg · m2) = 0.0705

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.