8.2-First Law of Motion

The First Law of Motion, also known as Newton's First Law, states that:

"An object at rest will remain at rest, and an object in motion will remain in motion, unless acted upon by an external unbalanced force."

This law defines the concept of inertia and helps us understand the behavior of objects when no external forces are acting on them. In simple terms, it implies that an object will continue its state of rest or uniform motion in a straight line unless a force changes that state.

The First Law is sometimes referred to as the Law of Inertia. Inertia is the property of an object that resists changes in its motion. The more massive an object is, the greater its inertia. This means heavier objects are harder to start moving or to stop once they are in motion.

Mathematically, the law can be expressed as:

If no external force acts on an object, the velocity of the object remains constant. In formula terms, this can be written as:

$\sum F = 0 \quad \Rightarrow \quad \frac{d}{dt} \vec{v} = 0$

Where:

• $\sum F$ is the sum of the external forces acting on the object (equal to zero).
• $\frac{d}{dt} \vec{v}$ represents the rate of change of velocity, which is zero when no external force is acting.

This means that if the net external force acting on an object is zero, there will be no change in its velocity. In other words, the object will either remain at rest or continue moving at a constant velocity along a straight line.

Inertia is a fundamental concept in understanding motion. It explains why passengers feel a jolt when a car suddenly accelerates or brakes—because their bodies tend to resist the change in motion caused by the car's movement.

Similarly, objects at rest, like a book placed on a table, stay at rest unless acted upon by a force such as a push. The table exerts an upward force on the book, which balances the gravitational pull, and thus, the book remains stationary.

The First Law of Motion laid the foundation for later developments in physics, especially Newton's Second and Third Laws, which further describe the relationship between force, mass, and acceleration.

Key points to remember:

• The First Law explains the concept of inertia.
• Objects do not change their state of motion unless acted upon by an external force.
• It applies to both objects at rest and objects in uniform motion.

In everyday life, examples of the First Law include:

• A ball resting on the ground stays at rest until you apply a force to move it.
• If you're in a moving car and it suddenly stops, your body continues to move forward until the seatbelt or another force slows you down.

Thus, the First Law of Motion introduces us to the idea that forces are necessary to change the motion of an object, and without a force, an object will maintain its current state, whether it's at rest or moving at a constant velocity.