## The Law of Inertia

In physics, a law is the result of experimental observation. The laws of nature can not be proved by mathematical manipulation of mathematical expressions, they are only supported by experimental observations.

The first scientist to recognize the law of inertia was Galileo Galilei. Galileo's conclusion was deduced after observing the motion of an object moving over two incline planes set as shown in Figure 2. The figure below shows Galileo's experiment in three different parts. In all parts, two inclined planes are placed opposite to each other, A and B. At the top of the inclined plane A, a ball is let roll freely toward the bottom of the inclined. The inclines A and B are placed in such a way that when the rolling object reaches the bottom of the first inclined, the object rolls smoothly over the second plane, B. In this experiment, Galileo's observes that no matter what is the slope of the incline B, the tendency of the rolling ball is to reach the height (level) from where the ball was originally released (dashed red level). Part I and Part II of Figure 2 illustrate this experiment for to different inclinations for plane B. As Galileo theorized, Part III shows the extreme case when the incline B is horizontal. In this case, the ball should roll forever because the ball can not reach the original height (red level) when no external force is applied to the rolling ball.

 Newton's Law -- Figure 2 -- Galileo's Inertia Experiment

Nevertheless, erroneously, Galileo Galilei excluded from the requirement of satisfying the law of inertia objects moving in circles (such as celestial objects). When circular motion is presented in xxx, it will be understood that circular motion also follows the same rules, in accordance with the law of inertia. The way in which the law of inertia is presently understood was firstly recognized by Rene Descartes.

As the result of these observations, the law of inertia can be stated:

If no net force acts on an object, the object maintains the same state of motion.

For an object, to maintain the same state of motion means that the vector velocity of the object is unchanged. Thus, the magnitude of the velocity is constant and the direction of motion is unchanged. An object at rest correspond to the special case of zero velocity.

The law of inertia implies that if no external force act on an object, when at rest, the object will stay at rest; and, when in motion the object will move in straight line with constant velocity.

In order to understand the law of inertia in practical situations, remember that friction is a force, Thus, imagine a wooden block sliding over a surface such as the floor of a classroom as compared to the same block sliding over the icy surface in an ice skating ring. Where does the block slide further? Of course, the block will slide the further on the skating ring.

 Mass

Definition of mass: Inertia is the tendency of an object to maintain the same state of motion. The mass is the quantity used to measure the inertia of an object. In fact, the relation is equivalent to the relation between height and tall.

How tall is an object? The answer to this question is the height of the object.

Similarly,

How much inertia an object has? It depends on how much mass the object has.

An object with a large inertia will have a large mass. If there were an object for which no force is required to change the state of motion, that object will not have inertia and no mass. Therefore, the minimal mass for an object is zero. Additionally, there is not such thing as objects with negative masses (minimal inertia correspond to zero mass). Experimentally, negative masses have never been observed. Thus all masses are positives.

The mass of an object is measured in Kilograms (kg) in the International System (SI) of measurements.

The following are the approximate masses of different objects:

 Mass (kg) Universe 1 × 1052 Milky Way Galaxy 7 × 1041 Earth 2 × 1030 Human 7 × 101 Mosquito 1 × 10-5 Hydrogen Atom 1.67 × 10-27 Electron 9.11 × 10-31

 Inertial Frame of Reference.

Suppose that you are inside a bus that it is being driven at constant velocity. In the center of the isle there is a soccer ball which is free to move. As long as the bus moves at constant velocity, the soccer ball stays at the same place at the center of the isle.

However, if the driver suddenly applies the break, the soccer ball will roll to the front of the bus without the application of a force. An observer inside the bus, observer A, will conclude that the ball does not obey the law of inertia. Is the observer right?

On the other side, for an observer on the street, observer B, the ball rolls because it obey the law of inertia. When the brakes are applied to the bus, the brake pads exert the necessary force to slow down the wheels and the bus. At the same time, there is not a force to slow down the ball; therefore, the ball will maintain the same state of motion without changing the velocity and moving faster than the bus reaching the front of the bus. In this example there are two observer, the one inside the bus for which the law of inertia is not valid, and the one on the street for which the law of inertia is valid. The last one is called an Inertial Frame of Reference.

Frames of reference where the law of inertia is valid are called inertial frames of reference. The frame of reference associated to the observer inside the bus is not an inertial frame of reference. In conclusion, accelerating frames of reference ARE NOT inertial frames of reference.

 1)

If you are carrying a heavy bag of groceries and bang your hand against the wall, the concept that most explains why you are hurt is

 N a) inertia b) acceleration c) resistance. d) gravity e) None of the above.

 2) J Inertia Q 2 PTF498

A truck is moving at constant velocity. Inside the storage compartment, a rock is dropped from the midpoint of the ceiling and strikes the floor below. The rock hits the floor

 a) ahead of the midpoint of the ceiling b) behind the midpoint of the ceiling c) more information is need to solve this problem N d) exactly below the midpoint of the ceiling e) None of the above.

 3) J Inertia Q 3 PTF39

The law of inertia fails when

 N a) The frame of reference is accelerating b) The frame of reference is moving with unknown constant velocity. c) The frame of reference is not moving. d) The mass of the object is unknown e) None of the above.

 by Luis F. Sáez, Ph. D. Comments and Suggestions: LSaez@dallaswinwin.com