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If we consider the case of Earth, inertia carries the Earth forward (inertia alone will make the Earth go out of orbit so gravity keeps it in orbit around the sun), but if we consider the case of a car, we usually say that momentum carries the car forwards after we let go off of the accelerator, but doesn't inertia also play a factor?

Inertia (Newton's First Law) is the resistance to a change in motion, and an object (such as the car) that is moving will not want to stop. Momentum also carries the car forward because $p=mv$ and the car has mass as well as velocity. So, is the car being kept in motion (after we let go off of the accelerator) due to inertia, momentum or both? And, in general, how do we decide when inertia or momentum keeps the object in motion?

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  • $\begingroup$ If you will objects having inertia is just describing the fact that without additional force, momentum won't change, a planet will keep moving or a rock will keep laying there. So that things have inertia is just a fact about how momentum behaves, they are not conceptually on the same level. $\endgroup$
    – Kuhlambo
    Aug 8, 2022 at 9:55
  • $\begingroup$ More to the question about the car: it is the principle of inertia (Newton 1.) that is keeping the momentum up, so that is moving the car, where it frictionless, inertia would keep the momentum constant for ever (like a space car would...). The $\endgroup$
    – Kuhlambo
    Aug 8, 2022 at 10:07

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How do we decide when inertia or momentum keeps the object in motion?

The principle of inertia and the law of conservation of momentum are just different names for the same thing. Momentum allows us to quantify inertia - the greater the momentum of an object, the more it “resists” attempts to change its velocity.

Note that as well as linear inertia measured by linear momentum, an extended object will also have rotational inertia measured by angular momentum.

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The car's inertia means that its velocity will remain unchanged until an outside force acts on it (aka Newton's 1st Law). Momentum leads to conservation of momentum, which leads directly to Newton's 3rd law. Thus, for a moving object that is not interacting with any outside forces, that object's inertia is responsible for preserving its state of motion.

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Inertia is the resistance an object experiences to changes in motion, nothing more. In space, any object will travel in a straight line as long as there are no forces acting upon it. In that case the object is "carried forward by momentum" and inertia plays no role.

A car experiences a lot of friction (rolling friction, internal friction in the engine, air friction etc.), so the momentum will slowly bleed off. Having high inertia means that this bleeding off will happen slowly. In other words, an object is always "carried forward" by momentum. The inertia of an object just says how hard it is too lose this momentum. In real life circumstances with friction having high inertia means that an object will generally travel further given the same starting velocity.

I put "carried forward" in quotes because from a physics perspective it is weird to think about it this way. The natural state of an object is to keep moving in straight line with constant velocity. Only when external forces are acting on an object will it change from this natural path.

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    $\begingroup$ I would maybe add that the natural state of an object is to keep constant momentum, which means straight line motion as well as sitting still, depending if we have 0 or nonzero momentum. $\endgroup$
    – Kuhlambo
    Aug 8, 2022 at 10:09
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You could say: "having inertia" is just an expression describing the fact that without additional force, momentum won't change, a planet will keep moving or a rock will keep laying there. Saying that things have inertia is just making an observation about how momentum behaves, they are not conceptually on the same level.

More to the question about the car: it is the principle of inertia (which is also a name for Newton 1.) that is keeping the momentum from changing, but it's the momentum that is moving the car. Where it frictionless, inertia would keep the momentum constant for ever (like it would for a space car...).

Feel free to ask in the comments if this is still unclear.

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