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

Question

In traveling to the Moon, astronauts aboard theApollo 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 15-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m .

1. Determine the angular acceleration. = ____ rad/s2

2. Determine the radial component of the linear acceleration of a point on the skin of the ship 6.0 min after it started this acceleration. ar = ____ m/s2

3. Determine the tangential component of the linear acceleration of a point on the skin of the ship 6.0 min after it started this acceleration. at = ____ m/s2

Explanation / Answer

initial angular speed, wi = 0

wf = 1 rev / min = 2 pi rad / 60 sec = 0.105 rad/s

t = 15 min = 15 x 60 sec = 900s

wf= wi + alpha*t

0.105 = 0 + 900 *apha

alpha = 1.167 x 10^-4 rad/s^2 ............Ans

2. angular speed after 6 min = 0 + (1.167 x 10^-4 x (6 x 60 sec))

w = 0.042 rad/s

a_r = w^2 r = 0.042^2 x 4.25 =7.50 x 10^-3 m/s^2

3. tangential linear acc. = alpha * r

r = 8.5/2 =4.25 m

a_t = 1.167 x 10^-4 x 4.25 = 4.96 x 10^-4 m/s^2

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