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 uniformly from no rotation to one revolution every minute during a 12 min time interval. The spacecraft can be thought of as a cylinder with a diameter of 9.4 m.

(a) Determine the angular acceleration.
rad/s2

(b) Determine the radial and tangential component of the linear acceleration of a point on the skin of the ship 3.0 min after it started this acceleration.
m/s^2

(c) tangential
m/s2

Explanation / Answer

(a) One revolution per minute is 1/60 revolution per second is 2/60 radians per second. To get to that angular speed in 12 minutes is an angular acceleration of:

= (2/60 rad/s)/720 s = 1.4544 * 10-4 s-2

(b) After 3 minutes, the angular velocity is: = (1.4544 * 10-4 s-2)(180 s) = 0.02618 s-1

so the radial acceleration is ar = 2r = (0.02618 s-1)2(4.7 m) = 3.221 * 10-3 m/s2

(c) The tangential acceleration is at = r = (1.4544 * 10-4 s-2)(4.7 m) = 6.8359 * 10-4 m/s2

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