AAMC6 #34 Rotational Equilibrium Question

[dbeast]

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Q: A solid body can only be in rotational equilibrium when:

A: Its external torques sum to zero

However, another answer choice was when "the body is in free-fall" which made me think of satellite orbits, and how they remain in the same position above earth by essentially free-falling at the same rate of the earth's rotation. I understand the right answer, but is this another form of rotational equilibrium? Or is there a different term used to describe this situation? Gracias!

 

[EpicBearMan]

That's an interesting question. I'm not sure if the satellite would be considered to be in rotational equilibrium. My first thought is that it would probably depend on if the satellite has rotational acceleration around its own axis. I can't think of any terms to describe the situation other than standard orbit. Perhaps someone else will come along with more knowledge on the topic.

The question itself is pretty straight-forward, free-fall certainly isn't a requirement for any object to be in rotational equilibrium.

 

[lorenzomicron]

The satellite in that case is not in rotational equilibrium because equilibrium demands that torques (forces) sum to zero. More specifically, the force of gravity does act on the satellite causing it to free fall, i.e. a torque, which produces the physical reality of orbit.

However, more intuitively, the satellite-earth system could be in rotational equilibrium only if its rotation about the earth was fixed; however, the orbit of the satellite is not fixed as it moves.