# Weight and Inertia (are they related?)

R. Feynman wrote in his lecture (The Feynman Lectures on Physics: Chapter-9)

"Weight and inertia are proportional, and on the earth’s surface are often taken to be numerically equal, which causes a certain confusion to the student. On Mars, weights would be different but the amount of force needed to overcome inertia would be the same."

I am not able to understand how weight and inertia are related because everywhere on internet, everyone is only showing the relation between inertia and mass.

So, is their any relation between them(if so please explain...) or is he wrong in his statement.

• What is the relationship between mass and weight? – user207455 Jul 10 at 16:24
• Weight of an object is mass times the acceleration it experiences I think – Kshitiz Sharma Jul 10 at 18:26
• What's the formula for "inertia"? – safesphere Jul 10 at 20:30
• I don't think inertia has any formula because it is only a cause or you can say a property of any object to resist any change in motion. However there is a term known as inertial mass which is almost same as gravitational mass and they have the same formula. – Kshitiz Sharma Jul 11 at 6:34

Weight and inertia are proportional to each other with the constant of proportionality being the strength of the local gravitational field or, equivalently, the absolute value of the acceleration that the frame of reference that the object is being measured in is undergoing.

So, on the surface of the Earth, there is a gravitational field whose absolute value is approximately constant, and is given by $$g \approx 9.8\,\mathrm{ms^{-2}}$$. This means that a mass of $$1\,\mathrm{kg}$$ has a weight of approximately $$9.8\,\mathrm{kg\,m\,s^{-2}} = 9.8\,\mathrm{N}$$.

Because of this approximate constancy of $$g$$ and the fact that almost everyone lives on the surface of the Earth, we often become lazy and talk about something 'weighing $$n\,\mathrm{kg}$$', and we have scales which read in kilograms or grams, or pounds or ounces, when in fact what these scales are doing is measuring force, not mass: on the Moon, all these scales would be wrong, because the constant is different there ($$g_\text{moon} \approx 1.6\,\mathrm{ms^{-2}}$$).

Inertia and mass, or inertial mass and gravitational mass, are always (we think) the same, and this is very important for theories of gravity.

Weight is the measure of how much force does gravitation exert on an object. It can be expressed in units of mass, by dividing by the Earth's standard gravity: $$\text{weight} = \frac{\text{gravitational force}}{9.80665\, m/s^2}$$

Inertia, or inertial mass, is a measure of how much force do you need to apply to an object to cause acceleration: $$\text{acceleration} = \frac{\text{force}}{\text{inertial mass}}$$

It turns out that the inertial mass also happens to affect how big the gravitational force acting on an object is: $$\text{gravitational force} = (\text{inertial mass})\cdot(\text{intensity of gravitational field})$$ but that's not a part of the definiton of inertial mass, that just happens to be a law of physics.

We have then $$\text{weight} = (\text{inertial mass})\cdot\frac{(\text{intensity of gravitational field})}{9.80665\, m/s^2}$$ If the object is affected by gravitational field of intensity equal to Earth's standard gravity, it will have weight equal to the inertial mass. This is however not true when the intensity of gravitational field is different, for example on Mars, and even on Earth the gravitational field varies from point to point.

I think what he's saying is that an object that is more massive (or weighty) has more mass and hence more inertia.

Actually, we must change the words from “light” and “heavy” to less massive and more massive, because there is a difference to be understood between the weight of an object and its inertia. (How hard it is to get it going is one thing, and how much it weighs is something else.) Weight and inertia are proportional, and on the earth’s surface are often taken to be numerically equal, which causes a certain confusion to the student. On Mars, weights would be different but the amount of force needed to overcome inertia would be the same.

As you can see that he clearly differentiates between the terms weight and inertia. What he's trying to mean is that in Mars too, an object that is more massive will have more weight than an object that is less massive.

However if you consider a body of some mass $$m$$ and perform your measurements in different gravitational fields then you'll get different values of weights but that doesn't mean that the inertia has changed. Inertia is a measure of an object's resistance to changes in its state of motion or rest which is equal to the mass of the body or the amount of matter it has.

In an uniform gravitational field the inertia of a body is directly proportional to its weight.