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 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determin (a) the angular acceleration, and (b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 7.0 min after it started this acceleration.

Explanation / Answer

...angular acceleration..." angular acceleration = (change in angular velocity) / time = (final ang. velocity - initial ang. velocity) / time The final angular velocity is 1 rev per minute. The initial angular velocity is zero. The time is 15 minutes. So: angular acceleration = (1 rev/min.) / (15 minutes) But they want the answer in "radians/sec²". So you need to convert the rev's to radians (1 rev = 2p radians); and the minutes to seconds (1 min = 60 seconds). So, after the conversion: angular acceleration = (2p radians/60sec) / (15*60 sec) Do the math. > "...radial and tangential component of the linear acceleration..." radial component of linear acceleration = (angular speed)² × R (where "R" is the radius of the cylinder, 4.6 meters). angular speed = (initial angular speed) + (angular acceleration) × time The "initial angular speed" is zero. The "angular acceleration" is what you calculated in Part "A". The "time" is 1 minute (60 seconds). Plug in the numbers. Tangential component of linear acceleration = (angular acceleration) × R You already have both "angular acceleration" and "R". Multiply.

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