Question

In traveling to the Moon astronauts aboard the Apollo spacecraft put themselves into a slow rotation in order to distribute the Sun's energy evenly. At the start of their trip, they accelerated from no rotation to 1.5 revolution every minute during a 13-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 7.5 m. a.)Determine the angular acceleration. b.) Determine the radial component of the linear acceleration of a point on the skin of the ship 4 min after it started this acceleration.

Answer 1

(a) As we know that the acceleration is simply the difference of speed over the difference of time.

Now the spacecraft went went from 0 rad/s to 1.5 revolution/min.

1.5 revol / min = 2pi / (1.5x60) rad/min = pi/45 rad/s

time, t = 13 min = 13 x 60 = 780 s

Therefore, the angular acceleration = (pi/45) / 780 = pi / (45x780) = 3.141 / (45x780) = 8.95 x 10^-5 rad/s²

(b) Now the radial acceleration is the centrifuge acceleration given by v²/r or rw².

w after 60 seconds = pi/(45x780) x (4x60) = pi/146.25 rad/s

so the acceleration is (7.5/2)(pi/146.25)² [Given that the diameter of the cylinder = 7.5 m, so radius r = 7.5/2 m]

= 0.00173 m/s²

Therefore, the radial component of linear acceleration after 4 min = 0.00173 m/s²