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1 Newton’s First Law of Motion: Inertia (chapter from an Open Stax textbook)

This is part of a chapter from Open Stax College Physics.  It is free, and it was legal for me to import this and adapt it for my course.  My questions, etc .

Learning Objectives

At the end of this section the student will be able to

• define mass and inertia
• define Newton’s First Law of Motion

Experience suggests that an object at rest will remain at rest if left alone, and that an object in motion tends to slow down and stop unless some effort is made to keep it moving. What Newton’s first law of motion states, however, is the following:

NEWTON’S FIRST LAW OF MOTION

A body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force.

Note the repeated use of the verb “remains.” We can think of this law as preserving the status quo of motion.

Rather than contradicting our experience, Newton’s first law of motion states that there must be a cause (which is a net external force) for there to be any change in velocity (either a change in magnitude or direction). We will define net external force in the next section. An object sliding across a table or floor slows down due to the net force of friction acting on the object. If friction disappeared, would the object still slow down?

The idea of cause and effect is crucial in accurately describing what happens in various situations. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt. If we spray the surface with talcum powder to make the surface smoother, the object slides farther. If we make the surface even smoother by rubbing lubricating oil on it, the object slides farther yet. Extrapolating to a frictionless surface, we can imagine the object sliding in a straight line indefinitely. Friction is thus the cause of the slowing (consistent with Newton’s first law). The object would not slow down at all if friction were completely eliminated. Consider an air hockey table. When the air is turned off, the puck slides only a short distance before friction slows it to a stop. However, when the air is turned on, it creates a nearly frictionless surface, and the puck glides long distances without slowing down. Additionally, if we know enough about the friction, we can accurately predict how quickly the object will slow down. Friction is an external force.

Key Takeaways

Newton’s first law is completely general and can be applied to anything from an object sliding on a table to a satellite in orbit to blood pumped from the heart.

Experiments have thoroughly verified that any change in velocity (speed or direction) must be caused by an external force. The idea of generally applicable or universal laws is important not only here—it is a basic feature of all laws of physics. Identifying these laws is like recognizing patterns in nature from which further patterns can be discovered. The genius of Galileo, who first developed the idea for the first law, and Newton, who clarified it, was to ask the fundamental question… “

What is the cause?” Thinking in terms of cause and effect is a worldview fundamentally different from the typical ancient Greek approach when questions such as “Why does a tiger have stripes?” would have been answered in Aristotelian fashion, “That is the nature of the beast.” True perhaps, but not a useful insight.

Mass

The property of a body to remain at rest or to remain in motion with constant velocity is called inertia. Newton’s first law is often called the law of inertia. As we know from experience, some objects have more inertia than others. It is obviously more difficult to change the motion of a large boulder than that of a basketball, for example. The inertia of an object is measured by its mass. Roughly speaking, mass is a measure of the amount of “stuff” (or matter) in something. The quantity or amount of matter in an object is determined by the numbers of atoms and molecules of various types it contains. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon. In practice, it is very difficult to count and identify all of the atoms and molecules in an object, so masses are not often determined in this manner. Operationally, the masses of objects are determined by comparison with the standard kilogram.

1: Which has more mass: a kilogram of cotton balls or a kilogram of gold?

Issac Newton said in a letter to Robert Hooke “If I have seen further it is by standing on the shoulders of Giants”.[1]

Section Summary

• Newton’s first law of motion states that a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This is also known as the law of inertia.
• Inertia is the tendency of an object to remain at rest or remain in motion. Inertia is related to an object’s mass.
• Mass is the quantity of matter in a substance.

Conceptual Questions

1: How are inertia and mass related?

2: What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?

Exercises

Type your own exercises here.  Here are the ones from Open Stax College Physics

1. A cleaner pushes a 4.00-kg laundry cart in such a way that the net external force on it is 8.00 N. Calculate the magnitude of its acceleration.
2. Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s2. (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.
3. In Figure 4.7 shown here: the net external force on the 24-kg mower is stated to be 51 N. If the force of friction opposing the motion is 24 N, what force F (in newtons) is the person exerting on the mower? Suppose the mower is moving at 1.5 m/s when the force F is removed. How far will the mower go before stopping?

Solutions

1: They are equal. A kilogram of one substance is equal in mass to a kilogram of another substance. The quantities that might differ between them are volume and density.

Conceptual Questions

1: How are inertia and mass related?  They are the same.   Mass is a measure of inertia.  The more mass the more inertia.

2: What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?   Mass is an intrinsic unchanging property.  Weight is a force and it depends on gravitational force.   You weigh 1/6 on the Moon but you have the same inertia.

Problems and Exercises

1. a = 2.00 m/s2
2. 56.0 kg
3. a) 75 N  b) (Jennifer’s notes.  I often dislike the wording used by OpenStax.  I would add more parts to this question. Namely, what is the net force acting on the mower when the person stops pushing, then what is the acceleration, then what is the distance travelled until it stops.)  That would be 24 N to the left, so the acceleration is a deceleration of 1.00 m/s2 to the left or -1.00 m/s2.    displacement = 1.1 m .

1.  Newton, Isaac. "Letter from Sir Isaac Newton to Robert Hooke"Historical Society of Pennsylvania

To the extent possible under law, Jennifer Kirkey and OpenStax have waived all copyright and related or neighboring rights to x-A-Learn PressBooks with Newton's Laws for C&BA, except where otherwise noted.