Mdthbs

Someone told me that it is not inertia, but I think it is inertia, because it will rotate forever. In my understanding, inertia is the constant motion of an object without external force. Am I wrong?

Is it inertia that a rotating object will rotate forever without external force? Someone told me that this is not inertia [...]

Well, sort of - it’s somewhat correct to say it is inertia, and somewhat correct to say it isn’t. One has to be precise with language! But there is some truth to what you were told.

“Inertia” generally refers to the tendency of objects to continue moving in a straight line with a fixed velocity unless an external force is applied to them. It is basically a single word that encapsulates Newton’s first law of motion. It is a very fundamental law of nature, and at some level, no one really knows why it’s true.

The different parts of the rotating object are definitely not moving in a straight line, and it’s not the case that no forces are acting on them. So there is more than just inertia at play.

What is happening with a rotating rigid body is that each part of the body “wants” to maintain its fixed velocity according to the law of inertia, but the rigidity of the body is preventing it from doing so (since the pieces of the body have different velocity vectors so with fixed velocities they would all fly off in different directions). At the microscopic level, each piece of the body is applying forces to the adjacent pieces. Those forces are causing those adjacent pieces to change their velocity, according to Newton’s second law of motion. The end result of this highly complicated process is surprisingly simple: the body rotates. But the underlying cause is more than just inertia.

Now, I said it’s also somewhat correct to say that it is inertia that’s making bodies keep rotating. This is because there is also a rotational analogue of inertia that in informal speech among physicists might still be referred to as “inertia” (although calling it rotational inertia is more appropriate, and it will also commonly be described under the terms “moment of inertia” or “conservation of angular momentum”, or even more fancy terms like “rotational symmetry of space + Noether’s theorem”, although each of these terms describes something a bit more complicated than just rotational inertia). This rotational inertia is the tendency of rotating rigid bodies to continue rotating at a fixed angular velocity in their center of mass frame, unless a torque is applied to them.

Rotational inertia differs from ordinary “linear” inertia in that it is a derived principle: it can be derived mathematically from Newton’s laws of motion, so in that sense it has (in my opinion) a slightly less fundamental status among the laws of physics. Rigid bodies don’t “want” to keep rotating in the same fundamental sense that particles “want” to keep moving in a straight line with a fixed velocity - they do end up rotating but it’s because of a process we understand well and can analyze mathematically (starting from Newton’s laws), rather than some mysterious natural phenomenon we observe experimentally and accept as an axiom without being able to say much more about why it’s true.

At its most basic, an object will rotate forever for the simple reason that there is no preferred direction in space.

Emmy Noether's theorem of 1918 explains how various conservation laws arise from from differentiable symmetries. It is a mathematical theorem, not a physics theory. Because of this mathematical certainty, it is one of the most important theorems in physics.

Noether's theorem explains how the conservation of angular momentum (rotation) is required on the assumption that rotation does not change the laws of physics. Similarly, energy is conserved if time does not change the laws, and conservation of linear momentum is caused by the absence of a preferred location.

As these assumptions have always been observed to hold, this gives a very strong proof for the conclusions (the conservation laws).

As Newton stated with his 1st law, an object without a force acting on it will keep moving with the same speed and direction. This is also known as the law of inertia. Inertia is the tendency of an object to resist acceleration. This is because no force is acting on it to affect acceleration.

For rotational motion, the version of this is the moment of inertia which is similar, but about the tendency to resist angular acceleration.

So it is inertia (the moment of inertia if rotation). It keeps rotating at constant angular frequency since it resists a possible change out of nowhere.

Without any applied torque the angular momentum of a rotating object is conserved.