# How many types of inertia are there?

I was looking for types of inertia, but I am confused. My book says there are three types of inertia, namely inertia of rest, inertia of motion, and inertia of direction. But when I searched for these types in good books like Halliday, Randall, Hewitt, Zemansky, no author has talked of types of inertia.

Now I feel as there are no types of mass, so there need not be types of inertia, as inertia is measure of mass.

Also, my book says that the earth going around the sun continuously is an example of inertia.

• Why vote this down ? Seems like a very reasonable request for a concept to be clarified by someone confused by a book. Commented Jan 3, 2022 at 9:41
• @StephenG Lately I have been seeing down votes in questions others think are "obvious", unfortunately. Commented Jan 3, 2022 at 12:02
• There's only one type of inertia, because there's only one type of mass (excluding negative mass, which somewhat is a theoretical construct so far). I suspect author confuses inertia with conservation of momentum $m \vec v=\text {const}$, which applies also to single body with zero net force. Speed is vector , so $\vec v = |v| \hat {\textbf {e}}$. Thus $\vec v = \text{const}$ means $|v|=\text {const}$ and $\hat {\textbf {e}} = \text{const}$, including possibility of $|v|=0$. So no need for 3 types of "constancy" either in momentum conservation. Commented Jan 3, 2022 at 12:59
• I'm confused by the answers. A Google search yields results for rotational inertia, translational inertia and static inertia. It is my impression that these are all intuitive and useful concepts. Commented Jan 3, 2022 at 14:36
• Which book? Is this section online? I'm asking because sentences that sound nonsensical often make more sense in context, or at least one can see the flaw in the author's argument leading to the statement. Commented Jan 4, 2022 at 4:58

My suggestion is you throw this book away, and use only "good books".

Whoever wrote this book has a very confused mind.

I can vaguely guess what the author might have had in mind when he mentioned these "three types", but trying to make sense of these very confused notions would only add to your confusion, not reduce it.

Also, while the revolution of the Earth around the Sun does involve inertia, the overall motion is certainly not exclusively due to inertia.

Just as a matter by curiosity (certainly not to buy it) what are the title and author of this book ?

EDIT

Maybe I should have given you more details earlier.

The inertia that, when no force is applied, keeps at rest a body at rest is the same that guarantees a body in motion "perseveres" in this motion at the same speed in the same direction. So what your book call "inertia of rest", "inertia of motion" (constant value of the speed in meters per second?) "inertia of direction" (which, combined with the previous one, is the only meaningful thing for a physicist, conservation of the "physical speed" which means both direction and value in meters per second). Distinguishing them as three "types of inertia" makes absolutely no sense.

Now about the Earth and the Sun. Before Copernicus (thank you, user4574), people believed the Sun went around the Earth. Now we know that it is the contrary, the Earth goes around the Sun. But this motion, called "revolution" takes a whole year and in combination with the tilt of the Earth's axis is responsible for the seasons. This motion does involve inertia, but also a force. It is the interaction of this force, the gravitation of the Sun, and the inertia of Earth that is responsible for it, not just some "rotational inertia" that by itself would keep the Earth to go around the Sun because it is now rotating around it.

There is really, however, such a thing as "rotational inertia". But not to go round another object: to keep an object rotating around itself (technically, around it own axis), like a rotating top, to keep rotating indefinitely if no (momentum of) force is applied on it. I am not going to elaborate on the notion of "momentum of force".

And indeed the Earth does rotate around its own axis. Not once a year but once a day. This is why we see the Sun rise and set every day. This daily motion does not mean that the Earth rotates around the Sun but rather rotates around its own axis, once a day.

And this daily motion, yes, is purely due to inertia, a different sort of inertia than the first one, technically called "conservation of angular momentum", but you can think about it, if you want, as a "rotational inertia" though to my knowledge nobody uses this term.

So yes, sunrise and sunset are phenomenons due to inertia, to the fact that the Earth keeps turning around its own axis, like a rotating top.

But it was not at all clear that you were referring to this daily motion in your question, since you were mentioning "going round the Sun", which I understood as the year-long revolution, which is not purely due to inertia.

• "Anyway, the revolution of the Earth around the Sun is certainly not an example of inertia." But it is though. The fact that the Earth doesn't move straight into the sun is because of inertia. Or at the very least we can all agree it's at least relevant. Commented Jan 3, 2022 at 12:06
• @Biophysicist I agree (without having to go into the complications proposed by Cleonis) with your point that inertia is relevant in the motion of the Earth around the Sun as understood by Cleonis, Hartmut Braun, you and me. But again psychologically I am afraid that is might be understood by the OP as some "motion inertia" that keeps, just by itself, the Earth going round and round the Sun forever just because this is what it does now. Commented Jan 3, 2022 at 14:53
• @Alfred Yes, that is an understandable worry to have. I was making my claim in the context of assuming gravity was already present, but the OP might not necessarily have that understanding nailed down yet. Thanks for the discussion :) Commented Jan 3, 2022 at 14:58
• Comments are not for extended discussion; this conversation has been moved to chat. Commented Jan 20, 2022 at 13:15

Newton’s first law (Wikipedia)

Law 1. A body continues in its state of rest, or in uniform motion in a straight line, unless acted upon by a force.

Inertia of rest ist the same as inertia of motion when you consider the value 0 for speed like any other value of speed. Inertia of motion is the same as inertia of direction if you consider that motion always has a direction.

Or in other words: velocity is a vector; it has direction and length. The vector does not change “unless acted upon by force”

Thus, your text book created some unnecessary confusion by stating that there are three kinds of inertia while there actually is only one kind.

Even more confusing (and wrong, as @Alfred already said) is the example of earth’s motion around sun.

• "Even more confusing (and wrong, as @Alfred already said) is the example of earth’s motion around sun." How is it wrong? It's at least a relevant concept as to why objects do not always move along the direction of the force. Inertia is why that happens. Commented Jan 3, 2022 at 12:09
• The OP indicates being unable to make sense of what is stated in the book. In your answer you invoke a abstract statement, Newton's first law. However, if the OP would be confident in the validity of Newton's first law the OP would not have submitted this question in the first place. The psychological dimension here is that the OP does not (yet) have the internalized understanding of the laws of motion that you have. Commented Jan 3, 2022 at 12:18
• @BioPhysicist Inertia, but also gravitation. Earth does not keep "going round the sun continuously" because it is presently going round and inertia is keeping it going round ! You also are increasing the OP's confusion ! Commented Jan 3, 2022 at 12:20
• @BioPhysicist It's not clear what you are trying to say. Objects accelerate in the direction of the force. Force can be at an angle to existing velocity, but the thing is: the existing velocity that you attribute is dependent on the choice of inertial coordinate system. Choice of inertial coordinate system is arbitrary because existing velocity is absent in the relation F=ma. You can always transform to an instantaneously co-moving inertial coordinate system. Your statement 'objects do not always move along the direction of the force' sidesteps the concept of relativity of inertial motion. Commented Jan 3, 2022 at 13:17
• @Alfred I completely agree. I am not saying inertia is the only reason, but it is a reason. Just like how we say the reason we do not slide around on the ground is friction, yet other forces need to be present (gravity and normal force) in order for us to actually be pressed against the ground for friction to work how it does. I implicitly assumed gravity was present when I said inertia is relevant, just like how we assume we are forced against the ground when we say friction is why we are able to not slide across the ground. Commented Jan 3, 2022 at 14:17

Most generally inertia is resistance to change. This can apply to your daily life too. For example sleep inertia is when you wake up groggy and a bit slow and you'd rather go back to sleep. Your body resists changing from being asleep to not being asleep.

The three types of inertia mentioned by your book are vague statements about how objects resist changing being at rest, changing their motion and changing their direction of motion$$^\dagger$$. Here I don't mean vague in a negative way, it's just a more conceptual, less precise way of stating things. These three types of inertia are things you have probably observed in your daily life and it is a way of categorising those observations.

It turns out that all those three types are actually the same thing. There is only one type of inertia: inertia of motion. And it is caused by mass. Being at rest is the same as moving with zero velocity. Changing your motion is the same as changing your velocity. Changing direction of motion is likewise the same as changing your velocity.

So the fact that these types of inertia are the same can be seen as a 'result' from physics. You're probably so used to this concept that you can't tell the difference. Personally I wouldn't bother splitting inertia up into three parts and naming them. I have also never heard of this before so it might just be something the author came up with.

$$\dagger$$ I'm not sure if inertia of direction refers to bodies not wanting to change direction or if it refers to objects spinning really fast not wanting to change orientation. Either way it shouldn't influence my story.

It sounds like your book was written by Aristotle. According to Einstein, physics works the same in all inertial reference frames. So the amount of force needed to accelerate a moving object is the same as that for one "at rest", and accelerating an object tangentially to its direction of motion takes the same amount of force as an acceleration normal to the direction of motion; given any acceleration, for each of these categories, there is some frame reference such that the acceleration is in that category. For instance, if you're looking at the force needed to accelerate a moving car, there is some frame of reference where the car is at rest, and so what is "inertia of motion" in one reference frame would be "inertia of rest" in another.

The author of this book may be confusing friction and inertia. The force needed to get an object at rest moving is more than that needed to keep it moving, but that is friction, not inertia. I'm not aware of any third coefficient of friction for acceleration normal to the direction of motion.

• Aristotle, yes, ! :) Commented Jan 4, 2022 at 6:52
• I gave you a +1 for "what is "inertia of motion" in one reference frame would be "inertia of rest" in another." It's the old sitting in a train in a station and seeing another train going by; you don't know whether the other train is moving relative to the station, or you are (or both), unless you can simultaneously see the station. Commented Jan 4, 2022 at 18:41

Compare the following two cases:
-you start running from standstill
-from running you slow yourself down to standstill

In both cases a force is required to cause change of velocity. It takes effort to get up to a speed; it takes effort to bring speed back down.

As we know, we call this common factor 'inertia'; a force is required to cause change of velocity

One is easily tempted to suppose that there is also a difference between the two cases. It is tempting to suppose that acceleration and deceleration are in some real sense different.

But then:
Here is something that one can actually try:
Let's say you are in a train carriage, a train carriage with room enough to run along the length. (Yeah, an actual train is too cramped for that, but work with me here.)

Let the train ride be so smooth that you cannot guess the speed of the train relative to the ground. Let the windows be blinded, so you cannot look outside. Let that train be moving at a speed that corresponds to normal running speed.

So: If you get up to running speed in that train carriage: it might be the case that the act of bringing yourself up to running speed has resulted in making yourself stationary with respect to the ground. There is no way of telling the difference.

Observations like that lead to the following generalization:
Inertia only tells you how much change of velocity there is, inertia never tells you how much velocity you have.

This is a rule to which no exceptions are known, for centuries now the physics community has been confident to think of it as a Law of physics:

Inertia only tells you how much change of velocity there is.

It doesn't get more fundamental than that.

According to you your book asserts three types of inertia. That assertion is in contradiction with one of the fundamental laws of motion.

The conclusion is inevitable: the author of that book must be very confused indeed.

There aren’t three “types” of inertia. Inertia is a property of mass in which remains at rest or continues to move at constant speed in a straight line unless acted upon by a net force, per Newton’s first law.

It appears your book is simply describing these three aspects of the first law ( rest, motion, direction). In my opinion the book shouldn’t refer to these as “types” of inertia.

Hope this helps

• See my comment to Hartmut Braun Commented Jan 3, 2022 at 11:13

Use Newton's laws here

Inertia of rest: "An object at rest stays at rest, unless a net force acts on it"

Inertia of motion: "An object in motion stays in motion, unless a net force acts on it"

Inertia of direction: An object does not change direction on it's own without a force. Centripetal acceleration can change an object's direction. Take that you are in a car. You curve and feel that you are being pushed outwards. That's "centrifugal force", a nonexistent force caused by your inertia of direction, as you are not curving with the car, but moving tangent to the curve.