Newton’s First Law and Inertia
Newton’s first law states that an object at rest stays at rest, and an object in motion continues to move at constant velocity in a straight line, unless acted on by a net external force; inertia is the tendency of an object to resist changes in its velocity, and its measure is mass. In brief: a net force of zero means zero acceleration, not zero velocity. The first law defines inertial frames of reference, in which it holds. Seat belts, head restraints and the way a passenger lurches forward when a bus brakes are everyday consequences.
For nearly two thousand years it was thought that a force is needed to keep a body moving. Galileo and Newton showed that this is wrong: forces change motion. This guide states the law, explains inertia and mass, discusses frames of reference, compares the first law with older ideas in a table, works through examples including a seat belt calculation and corrects common mistakes.
What does the first law say?
The law says: Every body continues in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed on it. In modern terms, if the net force on an object is zero (ΣF = 0), its velocity is constant. This includes two cases: an object at rest stays at rest, and an object moving stays moving at the same speed and direction. On Earth we rarely see this motion, because friction and air resistance are always present; a hockey puck on ice, or a spacecraft in deep space, comes close to the ideal.
The law also tells us that an object can be moving and have no net force: a car cruising at a constant speed on a straight road has a driving force equal to the resistive forces.
What is inertia?
Inertia is the property of matter that resists changes in its state of motion. The greater the mass, the greater the inertia: it is harder to start or stop a loaded truck than a bicycle. Mass is the quantitative measure of inertia (inertial mass), in kilograms. Inertia is not a force. Examples: a passenger is pushed back into the seat as a car accelerates (the body tends to stay at rest), passengers lurch forward as a bus brakes (the body tends to keep moving), dust is shaken from a carpet when it is beaten, and a tablecloth can be pulled quickly from under dishes, which hardly move because the force acts for a short time. Coins on a card on a glass drop into the glass when the card is flicked away.
What are inertial frames?
The first law holds in an inertial frame of reference: a frame that is not accelerating. A laboratory on Earth is approximately inertial for most purposes. In an accelerating car, objects appear to accelerate with no force on them (a coffee cup slides backward on the dashboard as the car accelerates), which shows that the car is not an inertial frame; to explain such motion, an observer in it would need to introduce “fictitious forces”.
Aristotle and Newton compared
| Question | Aristotle’s view | Newton’s first law |
|---|---|---|
| What keeps an object moving? | A continuing force | Nothing; no force is needed |
| Natural state of a body | Rest | Rest or constant velocity |
| What do forces do? | Maintain speed | Change velocity |
| Role of friction | Ignored or part of nature | A force that slows objects |
Worked example: inertia in action
- Cruising car. A car of mass 1,200 kg travels at a constant 25 m/s. The driving force is 600 N, and so the air resistance and rolling resistance together must be 600 N. The net force is 0, and the acceleration is zero.
- Seat belt. A passenger of mass 70 kg in a car traveling at 15 m/s stops with the car in a crash over a distance of 0.50 m. The deceleration is a = v2 ÷ 2s = 225 ÷ 1.0 = 225 m/s2. The force on the passenger is F = ma = 70 × 225 = 15,750 N. The belt supplies this force; without it, the passenger continues to move at 15 m/s until stopped by the dashboard or the windshield, over a much shorter distance and with a larger force.
- Inertia and mass. The same net force of 100 N applied to a 2 kg cart and to a 10 kg cart gives accelerations of 50 and 10 m/s2. The 10 kg cart has more inertia and responds less.
- Hockey puck. A puck sliding on ice at 10 m/s with negligible friction travels 100 m in 10 s without slowing noticeably, as the first law predicts.
How was the law discovered?
Aristotle believed that objects need a continuing force to move. Galileo, in the early 1600s, reasoned with balls rolling down one inclined plane and up another: they rise almost to the original height, whatever the slope of the second plane. If the second plane were horizontal, the ball would roll forever. René Descartes stated the principle in 1644, and Newton set it as the first law in the Principia (1687).
Which mistakes are common?
Mistake 1: Thinking that a moving object must have a net force
At constant velocity, the net force is zero.
Mistake 2: Treating inertia as a force
Inertia is a property of matter. It is not an extra force acting on the body.
Mistake 3: Believing that a force is needed to maintain motion in space
A spacecraft with its engines off continues to move at constant velocity.
Mistake 4: Confusing “no net force” with “no forces”
Several forces can act on the body, but they cancel each other.