5.2 — Newton’s first law — inertia

The first law

If the net force is zero, an object continues in its state of motion — at rest or with constant velocity.

\[ \vec F_\text{net} = \vec 0 \Rightarrow \vec v = \text{const} \]

Note: "constant velocity" means magnitude AND direction constant — a straight line at uniform speed.

Why this was a revolutionary discovery

Before Newton, Aristotle believed an object needs force to move. Push a ball; when you stop, it stops — so "the force wore off". Newton realized: force is needed to start or change motion, not to continue it. The ball stops because of friction with air and ground — without friction, it would roll forever.

Inertia — the tendency to resist change

Inertia: an object's intrinsic tendency to maintain its state of motion. Mass measures inertia — more mass, more resistance to change.

Example: pushing an empty cart is easier than a full one. More mass → more inertia → less acceleration for the same push.

Inertial reference frames

The first law is not valid in every frame. Only in inertial frames:

• Inertial: a frame where the first law holds
• Non-inertial: a frame that is itself accelerating or rotating

Non-inertial example: a decelerating car. A bag on the seat slides forward — to an observer inside, no visible force accelerated it. That's a "fictitious force".

Detecting an inertial frame

Release a free object. If it stays or moves uniformly, inertial. If it accelerates with no apparent force, non-inertial.

Everyday applications

1. Seat belts: during hard braking, the car decelerates but your body has inertia. Your body keeps its initial velocity forward — the belt applies force to make you decelerate with the car.

2. Bag on a car seat in a turn: the car undergoes centripetal acceleration; the bag doesn't (no force on the bag). From outside, the bag moves straight. From inside the car, the bag appears to move outward (fictitious centrifugal force).

3. Washing machine spin: water leaves — not by "centrifugal force", but because it has inertia and moves straight, while the drum's holes rotate.

A few notes and common mistakes

1. Inertia is not mass. Inertia is a property; mass is its measure. Like height (property) and centimeters (measure).

2. Constant velocity ≠ at rest. The first law covers both. A car at 100 km/h on a frictionless track needs no force to keep moving.

3. Inertia doesn't depend on speed. A heavy ball moving slowly has the same "inertia" as one moving fast. What's hard is changing its motion.

What you should be able to do

• State the first law in vector form
• Define inertia and mass
• Distinguish inertial vs non-inertial frames
• Explain everyday applications (belts, turns, washing machines) via inertia

Preview of §5.3

The second law — what happens if force is not zero? Answer: the object accelerates. Relation: \vec F_\text{net} = m\vec a — the most important equation in classical physics.

📚 See also: Halliday Vol 1, Ch 5, §5.2.

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