Inertia and Momentum

Inertia²

In everyday language, we speak of something or someone “having a large inertia” to mean, essentially, that they are very difficult to set in motion. This usage of the word “inertia” is consistent with the “law of inertia” which states, among other things, that an object at rest, if left to itself, will just remain at rest, but it goes a bit beyond that by trying to quantify just how hard it may be to get the object to move.

We do know, from experience, that lighter objects are easier to set in motion than heavier objects, but most of us probably have an intuition that gravity (the force that pulls an object towards the earth and hence determines its weight) is not involved in an essential way here. Imagine, for instance, the difference between slapping a volleyball and a bowling ball. It is not hard to believe that the latter would hurt as much if we did it while floating in free fall in the space station (in a state of effective “weightlessness”) as if we did it right here on the surface of the earth. In other words, it is not (necessarily) how heavy something feels, but just how massive it is.

Momentum²

For an object of (inertial) mass m moving, in one dimension, with velocity v, we define its momentum as

p = mv

(the choice of the letter p for momentum is apparently related to the Latin word “impetus”).

We can think of momentum as a sort of extension of the concept of inertia, from an object at rest to an object in motion. When we speak of an object’s inertia, we typically think about what it may take to get it moving; when we speak of its momentum, we typically think of that it may take to stop it (or perhaps deflect it). So, both the inertial mass m and the velocity v are involved in the definition.

We may also observe that what looks like inertia in some reference frame may look like momentum in another. For instance, if you are driving in a car towing a trailer behind you, the trailer has only a large amount of inertia, but no momentum, relative to you, because its velocity relative to you is zero; however, the trailer definitely has a large amount of momentum (by virtue of both its inertial mass and its velocity) relative to somebody standing by the side of the road.

Gea-Banacloche, J. (2019). University Physics I: Classical Mechanics. Open Educational Resources. Retrieved from https://scholarworks.uark.edu/oer/3