Clarification on Momentum vs Inertia in Exerting Force when Stopping

Question

I encountered a physics question in an exam four years ago that I believe may have had an incorrect answer key. I'm seeking clarification on the correct concept. The question was:

The property of moving object by virtue of which it exerts force on the object that tries to stop it is: A) Momentum B) Inertia

The answer key provided "Inertia" as the correct answer. However, after studying this topic in depth, I've come to believe that "Momentum" is the more accurate answer. Here's my reasoning:

Inertia is the resistance of an object to any change in its motion. While related to momentum, it doesn't specifically describe the property that causes a moving object to exert force when something tries to stop it. Momentum seems to be the key concept here because when an object is in motion and something tries to stop it, the change in momentum results in a force. This is described by Newton's Second Law of Motion, which states that the rate of change of momentum is equal to the force applied.

My questions are:

Is my understanding correct that momentum, rather than inertia, is the more accurate answer to this question? If so, could you explain why inertia might have been chosen as the answer, and how it relates to this scenario? If my understanding is incorrect, could you please explain why inertia would be the correct answer in this context?

Answer 1

In general, physics and all of science uses specific words with specific meanings in order to promote clarity of thought and avoid confusion. Here is an example of a question which, in my opinion, tries to undermine that goal by focusing on language over concept. I have a personal dis-taste for such questions.

Although Newton's Laws involve the principle of "inertia," it is never defined as a quantity. If we think of "rest" as zero velocity, and "motion" as nonzero velocity, the quantity that resists changes in velocity seems most analogous to mass. Additionally, considering that "moment of inertia" quantifies the distribution of mass about an axis, the analogy seems acceptable. But most would agree that the definition of "inertia" is more than just mass; rather, it is the whole concept quantified by $\Sigma F = m a$.

"[Linear] Momentum," understood as $m v$, or the time integral of $m a$ if $m$ is constant, is a vector quantity that is conserved in the case where no external forces are acting. Calculations involving momentum can be useful in some situations, the best example being elastic collisions. But it's also correct to say that the sum of all forces on a mass is equal to the time rate of change of the linear momentum. For problems where mass varies with time, for example, this is the correct way to think about the problem.

If you understand the principles involved, and can do the appropriate calculations and arrive at the correct answer for a given problem, then you understand that, although perhaps "Inertia" is a better choice, both concepts are intertwined and either selection could be correct.

Answer 2

If objects resist changes in motion, they do so in all states of motion. An object at rest also resists although it has no momentum. Hence, it would be more appropriate to relate it to inertia and not momentum.

Answer 3

Yes you are right for me, as inertia is resistance to force or change in motion but is not the force. Hence Momentum is more accurate answer as momentum is the force exerted on the opposing object.

Thank You