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1.2.1 · D5Newton's Laws & Dynamics

Question bank — Newton's first law — inertia, operational definition of force

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The pictures you need before the traps

Three ideas keep appearing in the answers below. Meet them once, visually, and the traps become easy.

Figure — Newton's first law — inertia, operational definition of force

Look at the figure: the magenta arrow is one object; its orange shadow (across) and violet shadow (up) are its two components. Constant velocity means the whole arrow — length AND direction — never changes. Change either one and the arrow is different, which is the heart of every circular-motion trap.

Figure — Newton's first law — inertia, operational definition of force

The free-body diagram above shows the book: gravity (violet, down) and the normal push of the table (orange, up) are equal-length arrows pointing opposite ways. They cancel to a zero net arrow — so the book is a free body at rest, exactly the first law's balanced case.

Figure — Newton's first law — inertia, operational definition of force

True or false — justify

A body with zero net force must be at rest.
False. Zero net force means constant velocity, and constant velocity includes any steady straight-line speed — rest is just the special case .
If an object is moving, some force must be pushing it.
False. This is Aristotle's error. Once moving, an object keeps moving with no net force; force is only needed to change the motion, not sustain it.
An object moving at constant speed always has zero net force.
False. "Constant speed" is not "constant velocity" — a body circling at fixed speed changes direction (see the inward change-arrow figure), so its velocity changes and a net (centripetal) force acts. See Uniform circular motion.
The first law is just the special case of with .
False. It does two extra jobs: it defines force operationally (as the cause of velocity change) and it asserts inertial frames exist — neither follows from Newton's second law — F=ma alone.
Heavier objects have more inertia.
True. Inertia is measured by mass, so more mass means more resistance to any change in motion — harder to start, stop, or turn.
Inertia is a force that keeps things moving.
False. Inertia is not a force at all; it is a property (the resistance to change in motion). No push is exerted — the object simply persists on its own.
In a braking bus, a real forward force throws the passenger ahead.
False. No forward force acts on the torso; it merely continues at the old speed by inertia while the bus decelerates beneath it. The "shove" is an illusion.
The first law holds in every reference frame.
False. It holds only in inertial frames. In an accelerating frame a free body appears to accelerate with no real force, so the law fails there — see Inertial vs non-inertial frames.
A frame is inertial if and only if a free body in it moves at constant velocity.
True. That is precisely the operational test the first law provides; frames where free bodies drift or curve are non-inertial.

Spot the error

"The dishes stay because the fast cloth exerts no friction on them."
Wrong reason. Friction does act, but only for the tiny time the cloth is under them, so the impulse (the total nudge) and hence the velocity change are negligible — their inertia does the rest.
"A cruising plane has zero net force, therefore its engines are off."
Wrong conclusion. Many forces act; they cancel. Thrust balances drag and lift balances weight, giving zero net force with the engines running hard.
"Constant speed in a circle obeys because speed doesn't change."
Error: the first law demands the full velocity vector (length and direction) be constant. Direction changes every instant, so velocity changes and a net inward force is required.
"On the carousel I feel flung outward, so an outward force is real."
The outward feeling is a pseudo-force, an artefact of describing motion in a rotating (non-inertial) frame. In the ground (inertial) frame the only real force is inward. See Pseudo-forces.
"Mass and weight are the same thing, so more inertia means more force from gravity here and on the Moon equally."
Mass (the measure of inertia) is fixed everywhere; weight is a force that depends on local gravity and changes between Earth and Moon — see Mass vs weight.
"A book stops on the table, proving motion needs a continuous force."
The book stops because of a hidden force, friction. Remove it (ice, air-track, space) and the book never stops, which is exactly what the first law predicts.

Why questions

Why does the law insist on a straight line and not just constant speed?
Because velocity is a vector (an arrow with direction): keeping the arrow's length while turning it still changes the velocity, which requires a net force — only straight-line motion at fixed speed is truly force-free.
Why is the first law called an operational definition of force?
It gives a test you can perform: watch a free particle; any change in its velocity reveals that a force acted. Force is detected by its symptom (acceleration), not seen directly.
Why can't the second law tell us which frames are valid?
presumes you already know real forces and a good frame. The first law supplies that footing by declaring which frames (inertial ones) are honest enough for the second law to apply.
Why do we say inertia is "measured by mass" rather than "equal to mass"?
Inertia is a qualitative property (stubbornness against change); mass is the quantitative number that captures how much of that stubbornness a body has.
Why does removing friction rescue Newton from Aristotle?
Aristotle confused "no net force" with "no force at all." Friction was the hidden decelerating force; delete it and motion persists forever, showing force changes motion rather than maintaining it. See Friction.

Edge cases

If the net force on a body is zero for one instant only, is it in uniform motion?
Not necessarily. Uniform motion requires over an interval; a single instant of zero net force (for example, the top of a vertical toss, where the upward-then-downward force momentarily transitions) permits acceleration just before and after, so velocity need not stay constant.
Can a body have zero velocity yet nonzero net force?
Yes. At the instant a tossed ball reaches its peak, but gravity still acts, so — momentary rest is not the force-free state the first law describes.
Is the Earth's surface a perfect inertial frame?
No, only approximately. Earth rotates and orbits, so it accelerates; tiny pseudo-forces (like the Coriolis effect) appear. For most bench experiments the deviation is negligible, so we treat it as inertial. See Inertial vs non-inertial frames.
A spacecraft drifts in deep space with engines off — which state of the first law is it in?
The uniform-motion state: with it coasts at constant velocity in a straight line indefinitely, the cleanest real example of inertia.
Does an object at rest experience no forces?
Not necessarily — it experiences no net force. A book on a table has gravity down and the normal force up, which cancel (see the free-body diagram); rest means the forces balance, not that they are absent.

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