A. Angular momentum is always conserved would be the correct answer.
This is because like linear momentum (mvmv), angular momentum (r×mvr×mv) is a conserved quantity, where rr is the vector from the center of rotation. For a skater holding a static pose, for each particle making up her body, the contribution in magnitude to the total angular momentum is given by mirivimirivi. Thus bringing in her arms reduces riri for those particles. In order to conserve angular momentum, there is then an increase in the angular velocity.
hope this helps!
The answer would be false
Missing question:
"Determine (a) the astronaut’s orbital speed v and (b) the period of the orbit"
Solution
part a) The center of the orbit of the third astronaut is located at the center of the moon. This means that the radius of the orbit is the sum of the Moon's radius r0 and the altitude (
) of the orbit:
This is a circular motion, where the centripetal acceleration is equal to the gravitational acceleration g at this altitude. The problem says that at this altitude,
. So we can write
where
is the centripetal acceleration and v is the speed of the astronaut. Re-arranging it we can find v:
part b) The orbit has a circumference of
, and the astronaut is covering it at a speed equal to v. Therefore, the period of the orbit is
So, the period of the orbit is 2.45 hours.