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 15-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 9.0 m .

A) Determine the angular acceleration

B) Determine the radial component of the linear acceleration of a point on the skin of the ship 7.0 min after it started this acceleration.

C) Determine the tangential component 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 = 2 radians); and the minutes to seconds (1 min = 60 seconds).

So, after the conversion:

angular acceleration = (2 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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