# How does Inertia opposes change in state?

The first line of Wikipedia states that Inertia opposes change in velocity. My teachers also told that Inertia opposes change in state of rest or motion.

But I would like to know how?

Suppose a body is at rest as seen from an inertial frame and a net external force is applied then according to the above definition, shouldn't every body oppose the acceleration caused from that force because that force will change its state from rest to motion?

If yes, then why don't we count inertia force when calculating the net acceleration of a body ? i.e why isn't:

$$F_{(net\; external)}= inertial\; force+ ma$$

• What do you mean by everybody ? May 26, 2021 at 7:54
• @Srijan M.T I meant to say everything with mass May 26, 2021 at 8:35

We already include inertia in that equation, so there’s no need for another term. The mass, m, is a quantification of the inertia of the body, which is why the acceleration that a given force produces is proportional to the mass (which is to say the inertia) of the body being accelerated. Without inertia, any net force would produce an infinite acceleration. The fact that inertial mass is exactly equivalent to gravitational mass is one of the deep mysteries of physics that no one really understands.

• so mass ( or inertia) opposes acceleration or change by decreasing its value from infinite to a finite value. Right ? Feb 12, 2021 at 8:02
• kindly respond if you are active.. ;) Feb 14, 2021 at 13:18
• @Astudent It’s not a question that can be answered, because the terms in which it’s phrased don’t make sense. What you need to know is F = ma. Feb 14, 2021 at 13:32
• what is not making sense for you in the comment ? Feb 14, 2021 at 13:38
• Mass doesn’t oppose acceleration, and doesn’t decrease its value, as those words are commonly understood. The relationship between them needs to be expressed in mathematics rather than in words, and is F = ma. Feb 14, 2021 at 13:42

Inertia is an intrinsic property of matter. The term inertia is used in two different senses. In the directional sense, it means "momentum". Think of it as suddenly stopping while traveling by car. You would move forward. Is there any physical force that makes you move forward, no, there isn't. This is why we don't have a special variable for inertia but use momentum to describe it quantitatively.

Inertia is also matter resisting acceleration, known as F=ma. Here, mass is what quantifies inertia.

Inertia has a broad definition, "Inertia opposes change in state of rest or motion". We don't have a physical external quantity opposing the change in motion. On the other hand, the definition expresses an intrinsic property of matter that we already know. It is therefore easily expressed by quantities we already know such as mass and velocity.

The first line of Wikipedia states that Inertia opposes change in velocity. My teachers also told that Inertia opposes change in state of rest or motion...shouldn't every body oppose the acceleration caused from that force because that force will change its state from rest to motion?

Changing from rest to motion is a change in velocity (the velocity changes from $$0$$ to not $$0$$), so there is no contradiction, although the Wikipedia version is more general and includes the other.

However, saying inertia "opposes" something is very qualitative. "Opposes" here doesn't mean "stops". We are essentially just saying "more inertia $$=$$ more 'resistance' ". Once you start learning more physics you can abandon/bolster your qualitative descriptions with more accurate, quantitative ones. "Inertia opposes change in motion" becomes simply $$F=ma$$.

• It might be clearer as a = F/m. The acceleration produced by a force is divided by (resisted by) the mass (inertia). Jul 25, 2021 at 5:23
• @ikegami Thanks! Yes, those are mathematically equivalent. Jul 25, 2021 at 9:37