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

Reach for Newton's laws of motion whenever you are setting up a mechanics problem with forces: free-body diagrams, vehicle motion, falling objects, friction, pulley systems, and many collision models all start here. The three laws answer three questions in order. 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.

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

Step 1: Choose The Object

Decide which single object or system you are analyzing before drawing any forces. Everything downstream depends on this choice.

Step 2: Identify External Forces

List the pushes, pulls, gravity, friction, tension, and normal forces acting on that object. This is where the first law lives: an object remains at rest, or keeps moving at constant velocity, unless a net external force acts. If all external forces balance, velocity stays constant, and constant velocity includes the special case of rest. The law is also called the law of inertia.

Step 3: Find The Net Force

Combine the forces as vectors, keeping direction explicit. Add all external forces first; the acceleration depends on the net result, not on any one force you happen to notice.

Step 4: Apply The Law That Fits

• Use the first law for equilibrium or constant velocity, when you want to test whether forces balance.
• Use the second law when you need acceleration from a known net force, or net force from a known acceleration. It says the net external force equals the rate of change of momentum; for constant mass that becomes $\vec{F}_{net} = m\vec{a}$. The acceleration points along the net force, a larger mass gives a smaller acceleration for the same force, and a larger force gives a larger acceleration for fixed mass.
• Use the third law when two objects interact and you need the force pair: if object A exerts a force on object B, then B exerts an equal-magnitude force in the opposite direction on A. Those two forces act on different objects, so they do not cancel when you analyze one object alone.

Step 5: Check The Condition

Make sure any shortcut, such as $\vec{F}_{net} = m\vec{a}$, is being used under the right condition; here, that mass is constant.

Full 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 is $5\ \mathrm{N}$ to the left. Find the acceleration and connect the result to all three laws.

Step 1 — object: choose the box. Step 2/3 — forces and net force: combine the horizontal forces,

Step 4 — apply the second law:

So the box accelerates right at $3\ \mathrm{m/s^2}$. Now read it through all three laws:

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

The pattern: first find the net force on one chosen object, then use the third law separately to identify the matching force on the other object.

Where Each Step Tends To Trip You Up

• Step 3 (net force): treating zero net force as zero velocity. Zero net force means zero acceleration, not zero velocity; the object could move at constant speed in a straight line.
• Step 3 again: using one force instead of the net force. Add all external forces as vectors first.
• Step 4 (third law): pairing the wrong forces. Weight and normal force are often equal in magnitude but are not a third-law pair, because they act on the same object. A true pair acts on two different objects.
• Step 5 (condition): forgetting that $F_{net} = ma$ is the constant-mass form. The deeper statement of the second law is about momentum.

A quick decision aid you can self-check against: the first law tests balance, the second law turns net force into acceleration (or back), and the third law identifies the pair when two objects interact. As a self-check, change the example so friction is $20\ \mathrm{N}$ instead of $5\ \mathrm{N}$. Then the net force is zero, the box has zero acceleration, and it keeps a constant velocity if already moving.

Frequently Asked Questions