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

Question

In traveling to the Moon, astronauts aboard theApollo 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 m rotating about its cylindrical axis.

Part A

Determine the angular acceleration of the ship.

Express your answer using two significant figures.

Part B

Determine the radial component of the linear acceleration of a point on the skin of the ship 4.5 minafter it started this acceleration.

Express your answer to two significant figures and include the appropriate units.

Part C

Determine the tangential component of the linear acceleration of a point on the skin of the ship 4.5 min after it started this acceleration.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A:

angular acceleration = (change in angular velocity) / time
= (1-0)/12 rev/min^2 = 1/12 rev/min^2

Now convert this in rad/s^2

So, the result is, (1/12)*(2*pi/60x60) = 1.454x10^-4 rad/s^2

Part B:

radial component of linear acceleration = (angular speed)² × R

Now, angular speed = (initial angular speed) + (angular acceleration) × time
= 0 + 1.454x10^-4 x (4.5x60) = 0.039 rad/s

Therefore, radial component of linear acceleration = 0.039^2x8.5 = 0.013 m/s^2

Part C:

Tangential component of linear acceleration = (angular acceleration) × R = 1.454x10^-4 x8.5 = 0.0012 m/s^2

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