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3.4.1.5MechanicsCore

Newton’s Laws of Motion

Newton’s three laws are the rules that connect the forces on an object to how it moves. The middle one, , is the single most used equation in mechanics — but the first and third laws are just as important for reasoning about what a force actually does.

40 min Video by Science Shorts 3.4.1 Force, energy and momentum
F = ma — AS/A-Level PhysicsWatch the full walkthrough before the notes below.
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What you'll be able to do

  • State Newton’s three laws of motion
  • Explain why an object with no resultant force keeps a constant velocity (inertia)
  • Use F = ma to link resultant force, mass and acceleration
  • Interpret Newton’s second law as the rate of change of momentum
  • Identify Newton’s third-law force pairs and avoid the common traps
1

First law — inertia

Newton’s first law: an object stays at rest, or continues at , unless acted on by a resultant force. The tendency to resist a change in motion is called , and mass is its measure.

This overturns the everyday intuition that a moving object needs a continuous force to keep going. In reality it only slows down because of resistive forces such as friction and drag — remove those and it would coast forever.

Tip — If the velocity is constant (including at rest), the resultant force must be zero. If the velocity is changing in size or direction, there must be a non-zero resultant force.

2

Second law — F = ma

Newton’s second law: the resultant force on an object equals its mass times its acceleration. Acceleration is always in the same direction as the resultant force.

More fundamentally, the resultant force equals the . For constant mass this simplifies to , but the momentum form is the one that underlies impulse and collisions.

Resultant force (N) = mass (kg) × acceleration (m/s²).
Force is the rate of change of momentum p = mv.
1Resultant force N in the direction of motion.
2Rearrange to .
3 m/s².
Answer m/s²
3

Third law — action and reaction

Newton’s third law: if object A exerts a force on object B, then B exerts an equal and opposite force on A. The two forces are the and act on .

For example, the Earth pulls a book down with a gravitational force; the book pulls the Earth up with an equal gravitational force. A rocket pushes gas backward; the gas pushes the rocket forward.

Tip — A book resting on a table: its weight (gravity) and the normal force are NOT a third-law pair — they act on the same object and are different types. The pair to the weight is the book’s gravitational pull on the Earth.

Equation recap

Newton’s second law for constant mass.
Force as the rate of change of momentum.
Weight — the gravitational force on a mass.

Common mistakes to avoid

Thinking a constantly moving object must have a forward force on it.
Constant velocity means zero resultant force (first law). A driving force only balances resistance; it isn’t needed to keep moving.
Putting the weight and the normal contact force together as a third-law pair.
Third-law pairs act on different objects and are the same type of force. Weight and normal act on the same object.
Using the individual forces in F = ma instead of the resultant.
Always find the resultant (net) force first, then divide by mass.
Confusing mass and weight.
Mass (kg) is the amount of matter and measures inertia; weight (N) is the gravitational force mg on that mass.

Key takeaways

  • First law: with zero resultant force an object stays at rest or moves at constant velocity (inertia).
  • Second law: resultant force = ma = rate of change of momentum; acceleration is along the resultant force.
  • Third law: forces come in equal, opposite pairs that act on different objects and are the same type.
  • Always work with the resultant force, and keep mass and weight distinct.

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