Newton's First Law of Motion
by aoum, Mar 18, 2025, 10:29 PM
Newton's First Law of Motion: The Law of Inertia
Newton's First Law of Motion, also known as the Law of Inertia, is the foundation of classical mechanics. It describes how objects behave when no external force acts on them. This law was first articulated by Sir Isaac Newton in his monumental work Philosophiæ Naturalis Principia Mathematica (1687).
1. Statement of Newton's First Law
In modern terms, Newton's First Law states:
Mathematically, if the net external force
acting on an object is zero, the object’s velocity 
remains constant:
![\[
\mathbf{F} = 0 \implies \mathbf{v} = \text{constant}.
\]](//latex.artofproblemsolving.com/6/1/9/619c4efd9513b2e0bc95a52a5d6bb306d3cd396e.png)
If the object is initially at rest (
), it stays at rest. If it is in motion, it continues to move in a straight line with constant speed.
2. Understanding Inertia
Inertia is the property of matter that resists changes to its motion. The mass of an object quantifies its inertia. More massive objects require larger forces to change their state of motion.
3. Mathematical Formulation
Newton’s First Law is a special case of the more general Newton’s Second Law:
![\[
\mathbf{F} = m \mathbf{a},
\]](//latex.artofproblemsolving.com/a/9/f/a9f88f527ccf6e528fa20d7dff8587543124d4da.png)
where:
When
, it directly follows that:
![\[
\mathbf{a} = 0 \implies \mathbf{v} = \text{constant}.
\]](//latex.artofproblemsolving.com/4/3/b/43b54bc42059a4f5c94971aa6b298cfc203ceb11.png)
4. Examples of Newton's First Law
5. Inertial Frames of Reference
Newton’s First Law only holds true in inertial frames of reference. An inertial frame is one in which an object not acted upon by a force moves in a straight line at constant speed.
6. Historical Context and Galileo’s Principle of Relativity
Newton’s First Law builds upon Galileo Galilei’s concept of inertia. Galileo observed that, in the absence of friction, objects maintain their velocity.
Galileo’s insight:
7. Applications of Newton’s First Law
Newton’s First Law has practical implications in engineering, physics, and everyday life:
8. Newton's First Law and Modern Physics
While Newton’s First Law accurately describes motion at everyday speeds, modern physics refines our understanding:
9. Conclusion
Newton’s First Law of Motion is a fundamental principle describing how objects behave when no net external force acts on them. It establishes the concept of inertia and lays the foundation for understanding motion and forces in classical mechanics.
References
Newton's First Law of Motion, also known as the Law of Inertia, is the foundation of classical mechanics. It describes how objects behave when no external force acts on them. This law was first articulated by Sir Isaac Newton in his monumental work Philosophiæ Naturalis Principia Mathematica (1687).
Artificial satellites move along curved orbits, rather than in straight lines, because of the Earth's gravity.
1. Statement of Newton's First Law
In modern terms, Newton's First Law states:
Quote:
An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external force.
Mathematically, if the net external force
acting on an object is zero, the object’s velocity 
remains constant:![\[
\mathbf{F} = 0 \implies \mathbf{v} = \text{constant}.
\]](http://latex.artofproblemsolving.com/6/1/9/619c4efd9513b2e0bc95a52a5d6bb306d3cd396e.png)
If the object is initially at rest (
), it stays at rest. If it is in motion, it continues to move in a straight line with constant speed.2. Understanding Inertia
Inertia is the property of matter that resists changes to its motion. The mass of an object quantifies its inertia. More massive objects require larger forces to change their state of motion.
- If no net external force acts on an object, its acceleration is zero:
![\[
\mathbf{a} = \frac{d\mathbf{v}}{dt} = 0.
\]](//latex.artofproblemsolving.com/3/7/c/37ce35671947b276927b6b20a709157e1c00da6d.png)
- For an object with mass
, if , by Newton’s Second Law:
![\[
m \mathbf{a} = 0 \implies \mathbf{a} = 0,
\]](//latex.artofproblemsolving.com/1/f/9/1f9641ffd5bd6db4c42e9603bd752dd86724d0e4.png)
which confirms no change in velocity.
![\[
\mathbf{a} = \frac{d\mathbf{v}}{dt} = 0.
\]](http://latex.artofproblemsolving.com/3/7/c/37ce35671947b276927b6b20a709157e1c00da6d.png)
,![\[
m \mathbf{a} = 0 \implies \mathbf{a} = 0,
\]](http://latex.artofproblemsolving.com/1/f/9/1f9641ffd5bd6db4c42e9603bd752dd86724d0e4.png)
which confirms no change in velocity.3. Mathematical Formulation
Newton’s First Law is a special case of the more general Newton’s Second Law:
![\[
\mathbf{F} = m \mathbf{a},
\]](http://latex.artofproblemsolving.com/a/9/f/a9f88f527ccf6e528fa20d7dff8587543124d4da.png)
where:
- is the net external force (a vector quantity).
- is the mass of the object (a scalar quantity).
is the acceleration of the object (a vector quantity).
is the acceleration of the object (a vector quantity).When
, it directly follows that:![\[
\mathbf{a} = 0 \implies \mathbf{v} = \text{constant}.
\]](http://latex.artofproblemsolving.com/4/3/b/43b54bc42059a4f5c94971aa6b298cfc203ceb11.png)
4. Examples of Newton's First Law
- A Sliding Hockey Puck: On a frictionless ice surface, a puck will continue moving in a straight line unless friction or another external force slows it down.
- Objects in Space: In the vacuum of space, where there is negligible friction, satellites and spacecraft continue moving indefinitely unless acted upon by gravitational forces or other influences.
- A Passenger in a Car: If a car suddenly stops, a passenger without a seatbelt continues moving forward due to inertia.
5. Inertial Frames of Reference
Newton’s First Law only holds true in inertial frames of reference. An inertial frame is one in which an object not acted upon by a force moves in a straight line at constant speed.
- Earth is approximately an inertial frame for most practical purposes.
- Accelerating and rotating frames (like a spinning carousel) are non-inertial and require the introduction of fictitious forces to explain motion.
6. Historical Context and Galileo’s Principle of Relativity
Newton’s First Law builds upon Galileo Galilei’s concept of inertia. Galileo observed that, in the absence of friction, objects maintain their velocity.
Galileo’s insight:
- Motion does not require a continuous force unless resisting factors (like friction) are present.
- Without external interference, natural motion is uniform and rectilinear (in a straight line).
7. Applications of Newton’s First Law
Newton’s First Law has practical implications in engineering, physics, and everyday life:
- Space Travel: Spacecraft continue moving through space without propulsion once they escape Earth’s gravity.
- Automotive Safety: Seat belts counteract inertia during sudden stops, preventing injury.
- Structural Stability: Objects in static equilibrium (like bridges) remain at rest if no unbalanced forces act on them.
8. Newton's First Law and Modern Physics
While Newton’s First Law accurately describes motion at everyday speeds, modern physics refines our understanding:
- Special Relativity: At relativistic speeds (close to the speed of light), Newtonian mechanics is replaced by Einstein’s theory of relativity.
- Quantum Mechanics: At microscopic scales, particle behavior is described by quantum laws, although inertia still applies in the classical limit.
9. Conclusion
Newton’s First Law of Motion is a fundamental principle describing how objects behave when no net external force acts on them. It establishes the concept of inertia and lays the foundation for understanding motion and forces in classical mechanics.
References
- Newton, I. Philosophiæ Naturalis Principia Mathematica (1687).
- Halliday, D., Resnick, R., & Walker, J. Fundamentals of Physics (2013).
- Wikipedia: Newton’s Laws of Motion
- AoPS: Newton’s First Law
March 2025