Newton's Three Laws are the foundation of mechanics, explaining why objects remain at rest, move, and how they interact with each other. The First Law explains when an object maintains its velocity; the Second links force, mass, and acceleration with the formula \(F = ma\); the Third describes how forces always occur in pairs. This page provides precise definitions of all three laws, their formulas, clear real-life examples, problem-solving guides, and an interactive trainer to test your knowledge.
What are Newton's Laws
Newton's Laws are three rules that describe the motion of any object under the influence of forces. They were formulated by the English scientist Isaac Newton in the 17th century and have since formed the basis of all classical mechanics: from the flight of a ball to the movement of planets.
In short, the meaning of each law is:
- First Law (Law of Inertia) — an object does not change its velocity on its own. To accelerate, stop, or turn it, a force is required.
- Second Law — the greater the force and the smaller the mass, the faster the object accelerates: \(a = \dfrac{F}{m}\).
- Third Law — forces always act in pairs: if one object pushes another, the second pushes the first with the same magnitude of force in the opposite direction.
These laws work together: the first introduces the concept of force, the second allows you to calculate it, and the third shows that force is always an interaction between two objects.
First, Second, and Third Law of Newton: Definitions and Formulas
Below are three cards: the definition of each law, its formula, and a clear real-life example.
Comparing Newton's Three Laws
To keep the laws straight, it's helpful to see them side-by-side: what each is about, its formula, and how to identify it in a problem.
| Law | Formula | What it says |
|---|---|---|
| First | $\vec{F}=0 \Rightarrow \vec{v}=const$ | Without force, an object keeps its velocity (inertia) |
| Second | $F = ma$ | Force causes acceleration; mass resists acceleration |
| Third | $\vec{F}_{12}=-\vec{F}_{21}$ | Forces occur in pairs between two objects |
Problem-solving with Newton's Laws
Problem 1. Finding acceleration (Second Law)
Condition: a force \(F = 10\) N acts on an object with mass \(m = 2\) kg. Find the acceleration.
Solution. Newton's Second Law applies: \(F = ma\). We solve for acceleration:
Answer: \(a = 5\) m/s². The acceleration is in the same direction as the force.
Problem 2. Finding force (Second Law)
Condition: an object with mass \(m = 4\) kg moves with an acceleration \(a = 3\) m/s². What force is accelerating it?
Solution. Directly from the Second Law:
Answer: \(F = 12\) N. You can also find the mass: \(m = \dfrac{F}{a}\).
Problem 3. Pairs of forces (Third Law)
Condition: a person pushes a wall with a force of 200 N. With what force does the wall act on the person?
Solution. According to Newton's Third Law, interaction forces are equal in magnitude and opposite in direction: \(\vec{F}_{12} = -\vec{F}_{21}\).
This means the wall responds to the person with a force of the same magnitude — 200 N, but directed in the opposite direction. This is why the person doesn't "fall through" the wall but can push off from it.
Important: these two forces are applied to different objects (one to the wall, the other to the person), so they do not cancel each other out.
Common mistakes with Newton's Laws
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Thinking that action and reaction forces (Third Law) cancel each other out, so "nothing happens."
These forces are applied to different objects: one to the first object, the other to the second. Only forces applied to the same object can cancel each other out. Therefore, the force pair from the Third Law never "cancels" motion.
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Confusing mass and weight: substituting weight in Newtons into $F = ma$ instead of mass in kilograms.
Mass \(m\) is the amount of matter, measured in kilograms, and is the same everywhere. Weight is the force with which an object presses on a support, measured in Newtons: \(P = mg\). The Second Law formula uses mass in kg.
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Thinking that if $F = 0$, the object must be at rest.
The First Law allows for two cases: the object is either at rest or moving at a constant velocity in a straight line. If the net force is zero, a moving object simply continues to move at the same speed, rather than stopping.
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Thinking that an object constantly needs force to maintain motion.
Force is needed to change velocity (accelerate, brake, turn), not just to move. In the absence of friction, an object would move forever without any force — this is the Law of Inertia.
Q&A
What is the difference between Newton's First and Second Laws?
The First Law describes a special case where the force is zero: the object maintains its velocity (at rest or moving uniformly). The Second Law is general: it shows what happens when the force is NOT zero and allows you to calculate acceleration using \(a = F/m\). Essentially, the First Law is the Second Law when \(F = 0\).
How can Newton's three laws be stated briefly?
First: without force, an object maintains its velocity. Second: acceleration equals force divided by mass (\(a = F/m\)). Third: objects act on each other with equal and opposite forces.
Do Newton's laws apply in weightlessness?
Yes. Weightlessness only means that the object does not press on a support (weight is zero), but mass and forces do not disappear. All three laws work in weightlessness: to accelerate an object, you still need force (\(F = ma\)), and pushing off creates a pair of forces (Third Law). This is why an astronaut can move by pushing off the wall of a station.
What is inertia in simple terms?
Inertia is an object's property of maintaining its velocity until a force acts upon it. The greater the mass, the greater the inertia and the harder it is to change the object's motion. Inertia is what throws a passenger forward during braking and backward during acceleration.
What are the units of force and what is 1 Newton?
Force is measured in Newtons (N). From the formula \(F = ma\): 1 Newton is the force that gives an object with a mass of 1 kg an acceleration of 1 m/s². That is, 1 N = 1 kg·m/s².
