Newton's Laws of Motion — First, Second & Third Law

Newton's laws of motion explain three core ideas in classical mechanics: motion stays the same when the net external force is zero, motion changes when a net external force acts, and interaction forces always come in equal-and-opposite pairs on different objects.

If you are solving a physics problem, that usually means three questions. Is the net force zero? If not, what is the net force? And which two objects form each interaction pair? Once those are clear, most intro mechanics problems become much easier to set up.

Newton's First Law: Zero Net Force Means Constant Velocity

Newton's first law says that an object remains at rest, or keeps moving at constant velocity, unless a net external force acts on it.

The important phrase is net external force. If all the external forces balance, the object's velocity stays constant. Constant velocity includes the special case of staying at rest.

This law is often called the law of inertia. Inertia is the tendency of an object to resist changes in its motion.

Newton's Second Law: Net Force Sets the Acceleration

Newton's second law says that the net external force on an object equals the rate of change of its momentum. For many introductory problems, where the mass stays constant, that becomes

$$\vec{F}_{net} = m\vec{a}$$

This means the acceleration points in the direction of the net force. If the same net force acts on a larger mass, the acceleration is smaller. If the mass is fixed and the net force increases, the acceleration increases.

The condition matters: the familiar form $F_{net} = ma$ is the constant-mass form.

Newton's Third Law: Interaction Forces Come in Pairs

Newton's third law says that if object A exerts a force on object B, then object B exerts an equal-magnitude force in the opposite direction on object A.

Those two forces act on different objects. That is the part students most often miss. Because they act on different bodies, they do not cancel when you analyze the motion of one object alone.

Worked Example: A Box Pushed Across the Floor

A $5\ \mathrm{kg}$ box is pushed across a floor with a horizontal force of $20\ \mathrm{N}$ to the right. Friction on the box is $5\ \mathrm{N}$ to the left. Find the box's acceleration and connect the result to all three laws.

Choose the box as the object. Then combine the horizontal forces:

$$F_{net} = 20 - 5 = 15\ \mathrm{N}$$

So by Newton's second law,

$$a = \frac{F_{net}}{m} = \frac{15}{5} = 3\ \mathrm{m/s^2}$$

So the box accelerates to the right at $3\ \mathrm{m/s^2}$.

Now interpret that result with all three laws:

• The first law tells you the box would keep a constant velocity only if the net external force were zero. Here it is not zero, so the motion changes.
• The third law tells you the box also pushes back on the person with a force of $20\ \mathrm{N}$ to the left. That reaction force acts on the person, not on the box, so it does not reduce the box's net force.

This is the main pattern to remember. First find the net force on one chosen object. Then use the third law separately to identify the matching force on the other object.

Common Mistakes With Newton's Laws

Treating zero net force as zero velocity

If the net external force is zero, the acceleration is zero. That does not mean the velocity must be zero. The object could be moving at a constant speed in a straight line.

Using one force instead of the net force

You should add all external forces as vectors first. The acceleration depends on the net result, not just on one force you happen to notice.

Pairing the wrong forces in the third law

Weight and normal force are often equal in magnitude in simple situations, but they are not a third-law pair because they act on the same object. A true third-law pair acts on two different objects.

Forgetting the condition behind $F_{net} = ma$

In introductory mechanics, that shortcut is usually correct because mass is constant. In more general cases, the deeper statement of the second law is about momentum.

When Newton's Laws Are Used

Newton's laws are the starting point for free-body diagrams, vehicle motion, falling objects, friction problems, pulley systems, and many collision models. They also support many orbital mechanics approximations when classical mechanics is a good model.

They work very well for many everyday engineering and physics problems. At very high speeds, very strong gravitational fields, or atomic scales, more advanced models are needed.

How To Choose the Right Law Fast

Use the first law when you want to test whether forces balance and motion stays constant. Use the second law when you need acceleration from a known net force, or net force from a known acceleration. Use the third law when two objects interact and you need to identify the force pair correctly.

Try Your Own Version

Change the example so the friction is $20\ \mathrm{N}$ instead of $5\ \mathrm{N}$. Then the net force is zero, so the box has zero acceleration and keeps a constant velocity if it is already moving. If you want step-by-step feedback after trying it yourself, compare your setup on a similar force problem in GPAI Solver.