In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselves

Question

In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun's energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 11-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.3m

Part A
Determine the angular acceleration.
Express your answer using two significant figures..
a=..?..rad/s^2

PART B
Determine the radial component of the linear acceleration of a point on the skin of the ship 7.0min after it started this acceleration.(m/s^2)

PARTC
Determine the tangential component of the linear acceleration of a point on the skin of the ship 7.0min after it started this acceleration.

Explanation / Answer

a) 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 15 min = 900 s So acceleration is pi/30/900 = pi/27000 rad/s² b) The radial acceleration is the centrifuge acceleration given by v²/r or rw². w after 60 seconds = pi/27000 x 60 = pi/450 rad/s so the acceleration is (9.2/2)(pi/450)² = 0.000224 m/s² The tangential acceleration is the angular acceleration times r. Since the tangential acceleration is consant and was determined to be pi/27000 rad/s² you have tangential acceleration = pi/27000 x 4.6 = 0.000535 m/s²

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