Newton's Laws of Motion

Newton's laws of motion describe the relationship between a body, the forces acting on it, and its resulting motion. They're the foundation of classical mechanics, used to explain and predict how objects move throughout the physical world.

Key Takeaways

• First Law (Inertia): objects at rest or in motion stay that way unless acted on by a net force.

• Second Law: F = ma — acceleration is directly proportional to net force and inversely proportional to mass.

• Third Law: every action force has an equal and opposite reaction force, and the two always act on two different objects — they never act on (or cancel within) the same object.

Newton's First Law: The Law of Inertia

Newton's First Law, also known as the Law of Inertia, states:

"A body in a state of motion or at rest will remain in that state unless acted upon by a net force."

This law introduces inertia — an object's tendency to resist changes in its state of motion. If an object is at rest, it stays at rest; if it's moving, it continues in a straight line at constant speed — unless a force causes it to change.

Example: A soccer ball lying on the ground stays there indefinitely if no one kicks it — that's inertia. Kick it, and you apply a force that sets it moving; once rolling, it continues to roll until friction or an obstacle stops it. Without a force, there's no change — objects don't start or stop moving on their own.

Newton's Second Law: F = ma

Newton's Second Law states:

"When a net force is applied to a body of mass m, the body will be accelerated in the same direction as the force applied. The acceleration is directly proportional to the net force and inversely proportional to the mass of the object."

This relationship is expressed by the equation:

F = ma

The greater the force applied to an object, the greater its acceleration — but the more massive the object, the more force is needed to achieve that same acceleration.

Example: Pushing an empty shopping cart is easy — a small force accelerates it readily. A cart full of heavy items needs a much larger force to reach the same acceleration. This illustrates the direct relationship between force and acceleration, and the inverse relationship between mass and acceleration for a given force.

Newton's Third Law: Action and Reaction

Newton's Third Law states:

"For every action, there is an equal and opposite reaction."

Whenever one object exerts a force on a second object, the second object exerts a force of the same magnitude, but in the opposite direction, back on the first — and these two forces occur simultaneously, always acting on two different objects.

Example: Standing on a skateboard and pushing against a wall, the force you exert on the wall is the action force. The wall pushes back on you with an equal force in the opposite direction — the reaction force — which is what sends you moving backward. This pairing shows up constantly: in walking (your foot pushes the ground, the ground pushes back, propelling you forward) and in rocket launches (engines push exhaust down, and the reaction force pushes the rocket upward).

Together, Newton's three laws provide a complete framework for understanding forces and motion: how objects resist changes in motion, how they accelerate under applied forces, and how forces always occur in pairs. Each law builds on the one before it.

Common MCAT Mistakes

• Thinking a net force is needed to keep an object moving at constant velocity. The First Law says the opposite — a net force is only needed to change motion. An object moving at constant velocity in a straight line has zero net force acting on it.

• Applying F = ma with the wrong force. F in F = ma is always the net force — the vector sum of every force acting on the object — not any single applied force in isolation.

• Treating action-reaction pairs as canceling out. The two forces in a Third Law pair act on two different objects, so they never cancel each other within a single free-body diagram. Forces that cancel on one object are separate, unrelated forces — not an action-reaction pair.

• Confusing "no net force" with "no forces at all." An object can have several forces acting on it and still be in equilibrium (First Law applies) as long as those forces sum to zero — for example, an object at rest on a table has both gravity and a normal force acting on it.

MCAT-Style Concept Check

Question: A swimmer pushes backward against the water with their arms, and their body accelerates forward. Which law best explains why the swimmer moves forward, and why?

• A) The First Law — the swimmer was at rest and needed a force to start moving.

• B) The Second Law — the water increases the swimmer's mass, changing their acceleration.

• C) The Third Law — the swimmer exerts a backward force on the water, so the water exerts an equal and opposite forward force on the swimmer.

• D) The Third Law — the swimmer's forward force and the water's backward force act on the swimmer and cancel out.

Answer: C

Explanation: This is a Third Law action-reaction pair: the swimmer's arms push backward on the water (the action force), and the water pushes forward on the swimmer with equal magnitude (the reaction force). The two forces act on two different objects — the water and the swimmer — so they never cancel; the reaction force on the swimmer is what causes their forward acceleration. Option A misapplies the First Law, which describes objects with no net force, not the cause of a specific motion. Option B is wrong because mass doesn't change. Option D incorrectly claims the two forces act on the same object.

FAQ

Does Newton's First Law mean force is needed to keep something moving?

No. The First Law says a net force is only required to change an object's motion — to start it, stop it, speed it up, slow it down, or change its direction. An object already moving at constant velocity in a straight line continues doing so with zero net force acting on it.

What exactly does "net force" mean in F = ma?

Net force is the vector sum of every force acting on an object, not any single force by itself. If multiple forces act on an object, F = ma uses their combined total, accounting for direction.

Why don't action-reaction force pairs cancel each other out?

Because the two forces in a pair act on two different objects, not the same one. Forces only cancel when they act on the same object and sum to zero; a Third Law pair always involves two separate objects, so each object only "feels" one of the two forces.

How are Newton's three laws related to each other?

The First Law describes what happens with zero net force (no change in motion). The Second Law quantifies what happens when there is a net force (F = ma). The Third Law explains where forces come from in the first place — every force is one half of an interaction pair between two objects. Together they form a complete description of forces and motion.