In travelling lo the Moon, astronauts aboard the Apollo spacecraft put spacecraf

Question

In travelling lo the Moon, astronauts aboard the Apollo spacecraft put spacecraft into a slow rotation to distribute the Sun's energy evenly (so one side would not become too hot). At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. Think of the spacecraft as a cylinder with a diameter of 8.5 in rotating about its cylindrical axis. Part B Determine the radial component of the linear acceleration of a point on the skin of the ship 10 min after it started this acceleration. Part C Determine the tangential component of the linear acceleration of a point on the skin of the ship 10 min after it started this acceleration.

Explanation / Answer

The acceleration is simply the difference of speed over the difference of time.

They went from 0 rad/s to 1 cycle/min = 2pi rad/min = pi/30 rad/s

12 min = 720 s

So acceleration is pi/30/720 = pi/21600 rad/s^2

b)

The radial acceleration is the centrifuge acceleration given by v^2/r or rw^2

w after 600 seconds = pi/21600 x 600 = pi/36 rad/s so the acceleration is (8.5/2)(pi/36)^2

Ar = 0.03233 m/s^2 = 3.233 x 10^-2 m/s^2

c)

The tangential acceleration is the angular acceleration times r.

Since the tangential acceleration is consant and was determined to be pi/210000 rad/s^2

tangential acceleration = pi/21600 x 4.25 = 6.2 x 10^-4 m/s^2

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