Question

# A small cylindrical spacecraft (mass of a few hundred kilograms) has run out of fuel, and...

A small cylindrical spacecraft (mass of a few hundred kilograms) has run out of fuel, and is tumbling slowly but uncontrollably at angular velocity ω, clockwise when seen from the front. The astronaut on board needs to stop it from rotating in order to keep its antenna lined up with Earth, so she can send a distress call.

Since the engines are out of fuel, she removes one of the engines from the spacecraft, climbs out on the side, and throws it off of the spacecraft.

Explain briefly how this will help her stop her spacecraft from tumbling

The angular momentum of the system must be conserved before and after the released of the engine. The projected engine will have angular momentum where m = mass of the engine, v = speed at which it is ejected and r = radius of the spacecraft.

This will effectively decrease the angular momentum of the spacecraft thereby decreasing the angular velocity of its rotation. If the ejection speed of the engine is large enough, the entire angular momentum can be transferred to the engine and the spacecraft will therefore stop rotating (though unlikely).

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