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I'm hoping any gravity or friction can be ignored.

I gather a spinning object is a non-inertial frame. I suppose that's because change of direction is acceleration. Continued acceleration requires continued force.

But apparently the constant rotation can also somehow be described as angular velocity. And the rotation described as having rotational inertia, aka moment of inertia. Inertia being resistance to change in velocity, meaning maintaining velocity unless forced.

Some explanations seem to result in a third explanation, conservation of angular momentum, explained abstractly in accord with a Noether's theorem about symmetry.

Qmechanic
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3 Answers3

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There are rotational analogs of Newton's 1st and 2nd laws that apply to rotating objects.

According to Newton's 1st law, objects in motion tend to stay in motion until acted on by a net force. This is attributed to the object's inertia, which resists acceleration. The rotational analog of inertia is moment of inertia, where every differential mass of a rotating object has its own inertia, depending on how far that differential mass is from the axis of rotation.

According to Newton's 2nd law, $F=ma$, or if you prefer, $a=\frac{F}{m}$. This says that an object must experience a net force to experience an acceleration, and the amount of acceleration is inversely proportional to the object's mass. The rotational analog of the 2nd law is $\tau=I\alpha$, where $\tau$ (aka torque) is the rotational equivalent of force, $I$ (aka moment of inertia) is the rotational equivalent of mass (or inertia), and $\alpha$ is the rotational equivalent of acceleration.

This means that rotating objects in frictionless environments continue to rotate due to their rotational inertia.

David White
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Which is true - objects keep spinning because of inertia; objects keep spinning because of centripetal force

The law of inertia, also called Newton’s first law, postulate in physics that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a net force. See https://www.britannica.com/science/law-of-inertia

So since the inertia of an object makes an object want to continue to move in a straight line at constant speed. It takes a net force to prevent that from happening.

Therefore, in the case of a spinning object, that net force is the centripetal force acting towards the center of the circular motion. So to answer your question, objects keep spinning because of the centripetal force, not inertia.

Here's another way to think about it. Think of the inertia of an object as a description of the way an object behaves when there is no net external force acting upon it. Which means, it remains at rest or moves at constant speed in a straight line.

Hope this helps.

Bob D
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Definitely inertia (although more accurately, "angular momentum", but definitely not the frames or internal forces). Angular momentum is the important conserved quantity here. (In detail, this is because space is invariant under rotation and invariant motions lead to a conserved momentum.)

The "inertia", in this case, "moment of inertia" for a rotating body, is a scale factor for the angular momentum, describing, for example, how much torque applied over what time is required to stop the object. And, for example, the moment of inertia could change dynamically as when a spinning skater pulls in their arms, but the angular momentum is still preserved.

Angular momentum would be conserved regardless of how the body is constructed. For example, if it was sand that was all of sudden let loose, and flew everywhere, it would fly off in such a way that angular momentum would still be conserved. But if it's a solid body, all of the pieces that would fly off are instead bound, and that binding (centripetal) force will be required for it to act as a solid body, but it's not what creates a conserved quantity. Also, again here, it's interesting to think of the skater: the angular momentum stays constant, while the forces also change.

tom10
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