# What relationship does mass and inertia have

### Relationship Between Mass and Inertia

The terms mass and inertia are both important concepts in classical as well as modern physics. The relationship between mass and inertia is. It has been said that mass is a measurement of inertia. We can illustrate this mathematically using force, momentum, and even energy. Momentum describes . A: These three concepts of inertia, mass, and weight are interconected. Intertia can be defined by Newton's first law, which states that "an object.

On the face of it, these are very different experiments and two very different properties. And yet, bodies of different inertias fall at the same acceleration in a gravitational field. If this really is true, then the only way that this can happen is if the two different properties - inertial mass and gravitational mass - are precisely proportional to one another.

We can then arrange our definitions so that the proportionality constant is unity and call the two equal.

## Using Inertia to Measure Mass

What is the next step beyond saying that gravity and inertia are both identical and equal? After a great deal more pondering, this lead Einstein to the general theory of relativity. In many lay explanations it is often implied that the principle of equivalence is the key result that lead to GTR and that GTR should somehow leap out as obvious to the reader from it.

This is not at all true. Equivalence was a very early hint. Having been the trumpeted all-important subject in Einsteins early papers of aboutit shrinks back into the background thereafter and its presence in GTR is actually quite subtle. One way of dealing with the hint of equivalence is to reflect that there is another important situation in classical physics where force on a body is proportional to its mass and that is in non inertial frames of reference such as in the often touted constantly accelerating space elevator.

- What is the Relationship Between Mass and Inertia

From the standpoint of a non-inertial observer, bodies experience forces of no obvious source in proportion to their inertial mass, exactly as happens for gravity. So perhaps the surface of the Earth is not an inertial frame? Indeed in classical general relativity, this is exactly what is happenning. General relativity postulates that space and time form an in general curved in a very technical sense - don't expect to grasp this notion with simple visual pictures; see also here manifold and that the motion of free bodies is along geodesics in this manifold.

Galileo reasoned that any difference between initial and final heights was due to the presence of friction.

Galileo postulated that if friction could be entirely eliminated, then the ball would reach exactly the same height. Galileo further observed that regardless of the angle at which the planes were oriented, the final height was almost always equal to the initial height.

If the slope of the opposite incline were reduced, then the ball would roll a further distance in order to reach that original height. Galileo's reasoning continued - if the opposite incline were elevated at nearly a 0-degree angle, then the ball would roll almost forever in an effort to reach the original height. And if the opposing incline was not even inclined at all that is, if it were oriented along the horizontalthen Newton's first law of motion declares that a force is not needed to keep an object in motion.

Slide a book across a table and watch it slide to a rest position. The book in motion on the table top does not come to a rest position because of the absence of a force; rather it is the presence of a force - that force being the force of friction - that brings the book to a rest position. In the absence of a force of friction, the book would continue in motion with the same speed and direction - forever!

### general relativity - What is the relationship between gravity and inertia? - Physics Stack Exchange

Or at least to the end of the table top. A force is not required to keep a moving book in motion. In actuality, it is a force that brings the book to rest. Mass as a Measure of the Amount of Inertia All objects resist changes in their state of motion.

All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object.

## Inertia and Mass

The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion. Suppose that there are two seemingly identical bricks at rest on the physics lecture table.