1. Statement of the First Law

Newton’s First Law states:

An object remains at rest or continues moving with constant velocity unless acted upon by a nonzero net external force.

This law describes the natural behavior of objects when forces are balanced.

2. Meaning of the Law

The first law tells us:

• objects do not naturally speed up, slow down, or change direction on their own
• motion changes only when a net external force acts

Two possible situations:

(1) Object at Rest

If the net force is zero:

\(\Sigma\vec{F}=0\)

the object remains at rest.

(2) Object in Motion

If the net force is zero:

\(\Sigma\vec{F}=0\)

the object continues moving with constant velocity.

Constant velocity means:

• constant speed
• constant direction

Thus acceleration is zero.

3. Relation to Acceleration

From mechanics:

\(\vec{a}=0\)

when

\(\Sigma\vec{F}=0\)

So balanced forces produce no acceleration.

4. Inertia

Newton’s First Law is often called the Law of Inertia.

Inertia

Inertia is the tendency of an object to resist changes in its motion.

• objects at rest resist moving
• moving objects resist changes in velocity

5. Mass and Inertia

Mass measures inertia.

• larger mass → greater resistance to acceleration
• smaller mass → easier to accelerate

Thus mass quantifies how difficult it is to change motion.

6. Equilibrium

When the net force is zero, the object is in equilibrium.

Two types:

Static Equilibrium

Object remains at rest.

Dynamic Equilibrium

Object moves with constant velocity.

7. External vs Internal Forces

Newton’s First Law concerns external forces.

Internal forces within a system cannot change the motion of the entire system’s center of mass.

8. Examples

Example 1: Book on a Table

Forces on the book:

• gravity downward
• normal force upward

Since forces balance:

\(\Sigma\vec{F}=0\)

the book remains at rest.

Example 2: Hockey Puck on Ice

A puck sliding on nearly frictionless ice continues moving at nearly constant velocity because the net horizontal force is approximately zero.

Example 3: Passenger in a Car

When a car suddenly stops, passengers continue moving forward due to inertia.

Seat belts provide the external force needed to change motion safely.

9. Inertial Reference Frames

Newton’s First Law defines an inertial reference frame.

An inertial frame is one in which:

• objects obey Newton’s laws
• objects with zero net force move with constant velocity

Accelerating frames are generally non-inertial.

10. Physical Importance

Newton’s First Law establishes that:

• force is connected to changes in motion
• constant motion requires no net force
• acceleration results from unbalanced forces

It forms the conceptual foundation for Newton’s Second Law.

Summary

Newton’s First Law:

An object remains at rest or moves with constant velocity unless acted upon by a net external force.

Key ideas:

\(\Sigma\vec{F}=0 \Rightarrow \vec{a}=0\)

• balanced forces produce no acceleration
• inertia resists changes in motion
• mass measures inertia

This law introduces the fundamental relationship between force and motion in mechanics.