1.6 - Newton's First Law

Introduction

Newton's First Law of Motion, also known as the Law of Inertia, is one of the fundamental principles of classical mechanics. It describes the behavior of objects when no net force acts upon them, establishing the concept of inertia—the tendency of objects to resist changes in their state of motion. This law provides the foundation for understanding motion and forces in physics.

Newton's First Law (Law of Inertia):

An object at rest will remain at rest, and an object in motion will continue in motion with constant velocity (constant speed in a straight line), unless acted upon by a net external force.

In mathematical terms, if the net force on an object is zero:

$$\mathbf{F}_\text{net} = \mathbf{0} \quad \Rightarrow \quad \mathbf{v} = \text{constant}$$

This means that if $\mathbf{v} = \mathbf{0}$ initially, the object remains at rest. If $\mathbf{v} \neq \mathbf{0}$ initially, the object continues moving with that same constant velocity.

Key Concepts

Inertia

Inertia is the property of matter that resists changes in motion. It is not a force, but rather an intrinsic property of all objects with mass. The more massive an object, the greater its inertia—the more it resists changes to its state of motion.

Understanding Inertia:
  • Objects at rest tend to stay at rest: A book on a table doesn't spontaneously start moving. It requires a force to overcome its inertia and set it in motion.
  • Objects in motion tend to stay in motion: A hockey puck sliding on ice continues moving in a straight line at constant speed (ignoring friction) because there's no net force acting on it.
  • Mass is a measure of inertia: A more massive object (like a truck) has more inertia than a less massive object (like a bicycle), meaning it's harder to accelerate or decelerate.

Net Force

The net force (or resultant force) is the vector sum of all forces acting on an object:

$$\mathbf{F}_\text{net} = \sum_i \mathbf{F}_i = \mathbf{F}_1 + \mathbf{F}_2 + \mathbf{F}_3 + \cdots$$

Newton's First Law applies when the net force is zero. This can occur in two situations:

Constant Velocity

When Newton's First Law states that an object moves with "constant velocity," it means both:

This is equivalent to saying the acceleration is zero:

$$\mathbf{a} = \frac{d\mathbf{v}}{dt} = \mathbf{0}$$

Historical Context

Newton's First Law was a revolutionary idea that challenged the Aristotelian view of motion, which held that objects naturally come to rest. Galileo Galilei had earlier proposed similar ideas about inertia, and Newton formalized and generalized these concepts in his Principia Mathematica (1687).

Galileo's Contribution:

Galileo observed that objects rolling down an inclined plane would roll up another plane to nearly the same height, regardless of the angle. He reasoned that on a perfectly smooth, horizontal surface, an object would continue moving indefinitely with constant velocity. This insight laid the groundwork for Newton's First Law.

Examples and Applications

Example 1: A Book on a Table

A book resting on a table remains at rest because the net force on it is zero. The gravitational force pulling it downward is exactly balanced by the normal force from the table pushing it upward. Since $\mathbf{F}_\text{net} = \mathbf{0}$, the book's velocity remains zero (it stays at rest).

Example 2: A Hockey Puck on Ice

A hockey puck sliding on smooth ice (where friction is minimal) continues moving in a straight line at constant speed. The net force is approximately zero (gravity is balanced by the normal force, and friction is negligible), so the puck maintains its constant velocity as predicted by Newton's First Law.

Example 3: Objects in Space

In deep space, far from any massive objects, a spacecraft with its engines off will continue moving with constant velocity indefinitely. There are no significant forces acting on it, so it maintains its motion according to Newton's First Law.

Example 4: Passengers in a Moving Vehicle

When a car suddenly stops, passengers lurch forward. This is because their bodies, following Newton's First Law, tend to continue moving forward with constant velocity. The car stops due to friction, but the passengers' inertia causes them to continue their forward motion until the seatbelt or dashboard applies a force to stop them.

Example 5: A Ball Rolling on a Frictionless Surface

If a ball is given an initial push on a perfectly frictionless horizontal surface, it will roll forever at constant speed in a straight line. The net force is zero (gravity is balanced by the normal force, and there's no friction), so the ball's velocity remains constant.

Common Misconceptions

Newton's First Law is remarkably unintuitive. It appears to violate our everyday experience because because it is exceedingly difficult to find situations where there is no friction, no air resistance, etc. Thus, there is almost always a non-zero net force acting on everything we see. This is why Aristotle's view of motion (which states that objects naturally come to rest and which violates Newton's First Law) is so appealing to our common sense. Some common Aristotelian misconceptions include the following:

Relationship to Other Laws

Connection to Newton's Second Law

Newton's First Law is actually a special case of Newton's Second Law. The Second Law states:

$$\mathbf{F}_\text{net} = m\mathbf{a}$$

When $\mathbf{F}_\text{net} = \mathbf{0}$, we get $m\mathbf{a} = \mathbf{0}$. Since mass $m \neq 0$, this implies $\mathbf{a} = \mathbf{0}$, which means $\mathbf{v} = \text{constant}$—exactly what the First Law states.

Inertial Reference Frames

Newton's First Law also serves to define what we call an inertial reference frame. An inertial frame is one in which Newton's First Law holds true. In non-inertial frames (accelerating or rotating frames), objects appear to violate the First Law unless we introduce fictitious forces.

Practical Applications

Understanding Newton's First Law is crucial in many practical situations:

Summary

Key Takeaways:
  • Newton's First Law states that an object at rest stays at rest, and an object in motion continues with constant velocity, unless acted upon by a net external force.
  • Inertia is the property of matter that resists changes in motion. More massive objects have greater inertia.
  • The law applies when the net force is zero, which can occur when no forces act or when forces cancel out.
  • Constant velocity means both constant speed and constant direction (straight-line motion).
  • Newton's First Law defines inertial reference frames—frames in which the law is valid.
  • The First Law is a special case of the Second Law when the net force is zero.
  • In everyday life, friction and other forces often mask the true behavior described by this law, but in the absence of net forces, objects maintain constant velocity.