Newton's laws of motion

Newton's first law

• An object stays at rest, or keeps moving at constant velocity, unless an unbalanced force acts on it.
• The tendency to resist a change in motion is called inertia, and mass is the measure of inertia.
• Consequences worth stating in answers:
  • a moving object needs no force to keep it moving — only to change its motion,
  • an object slows down because of friction or drag, not because its "force runs out",
  • constant velocity means balanced forces, and balanced forces mean constant velocity.

Newton's second law

• An unbalanced force produces an acceleration in the direction of that force.

$$F_{\text{net}} = ma$$

• $F_{\text{net}}$ — the net (unbalanced) force in newtons (N)

• $m$ — mass in kilograms (kg)

• $a$ — acceleration in m s⁻² (in the same direction as $F_{\text{net}}$)

• For a fixed mass, acceleration is proportional to the net force — double the net force, double the acceleration.

• For a fixed force, acceleration is inversely proportional to mass — double the mass, halve the acceleration.

• One newton is the force that accelerates $1$ kg at $1$ m s⁻².

• The force in $F = ma$ is always the net force. Substituting a single applied force while ignoring friction is the most common source of wrong answers in this whole standard.

Newton's third law

• For every force there is an equal and opposite reaction force.

• The two forces of a Newton's third law pair:

  • are always the same size,
  • act in opposite directions,
  • are the same type of force,
  • and — the crucial part — act on two different objects.

• Describe a pair using the "A on B / B on A" form:

  • the ground pushes up on the runner; the runner pushes down on the ground,
  • the Earth pulls down on the ball; the ball pulls up on the Earth.

• Because the two forces act on different objects, they never cancel each other out. Only forces on the same object can cancel.

Telling a third-law pair from balanced forces

This distinction is examined almost every year:

	Third-law pair	Balanced forces
Act on	two different objects	the same object
Always equal?	yes, always	only when the object is not accelerating
Same type of force?	yes	usually not
Example	book pushes down on table / table pushes up on book	weight of book down / normal force from table up

• The weight of a book and the normal force on it are not a third-law pair — they act on the same object (the book), and they are different types of force. They happen to be equal only because the book is not accelerating.