(1) In traveling to the Moon, astronauts aboardthe Apllo spacecraft putthemselve
ID: 1671329 • Letter: #
Question
(1) In traveling to the Moon, astronauts aboardthe Apllo spacecraft putthemselves
into a slow rotation to dsitribute the Sun's energy evenly.At the start of their
trip, they accelerated from no rotation to 1 revolution perminute during a 12-
min time interval. We can approximate the spacecraft as acylinder with mass
50 (metric) tons and a diameter of 8.5m. Calculate (a) theangular acceleration,
(b) the torque needed to produce such an acceleration, and(c) the magnitude of
the linear acceleration of a point on the skin of the ship5 min after it started
accelerating.
Explanation / Answer
(a) the angular acceleration, = /t= 2 - 1=2(1rpm /60s) - 0= (1/30) rad/s t= 12 x 60= 720s finally = /t= (1/30) / 720= =1.45 x10-4rad/s2 (b) the torque needed to produce such an acceleration,and = I I= mR2 ( for spacecraft as a cylindershell) or it is I= 0.5mR2 ( for spacecraft as a solid cylinder) =mR2 =50x103 (8.5/2)2 46.3x10-6 = 41.8 N m for a sylindershell or = 20.9 Nm for a sylinder (c) the magnitude of the linear acceleration of a point on theskin of the ship 5 min after it started accelerating. a = aT2 +ac2) aT= (at 5 min) R since constant acceleration was applied aT= 1.45x10-4 x (8.5 / 2) aT= 6.18 x10-4m/s ac = V2/R and since V=R ac = 2 R = t at 5 minutes the angular speed will be = 46.3 x10-6 x 5x60 = 0.0139 rad/s now ac = 0.0139 2 (8.5/2) ac = 8.20x10-4 m/s2 finally a = aT2 +ac2) a= 10.3x10-4m/s2 finally a = aT2 +ac2) a= 10.3x10-4m/s2
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