① Newton's First Law (Law of Inertia): An object remains at rest or in uniform motion unless acted upon by a net external force.
Section 02
The Idea, Step by Step
Start simple: things don't change their motion on their own
Imagine a hockey puck sitting on smooth ice. It just sits there. Give it a
push and it glides — and on perfect ice it would keep gliding forever, in a
straight line, at the same speed. Nothing speeds it up, slows it down, or
turns it unless something pushes or pulls it. That "something" is a
force. This is the whole heart of Newton's First
Law: left alone, an object keeps doing what it was already doing.
The reason your bike eventually stops isn't that motion "runs out" — it's that
friction and air are quietly pushing back on you.
Build it up: how much does a push change things?
Now push two shopping carts: an empty one and a full one. The same push
speeds up the empty cart quickly but the heavy cart barely budges. So how
fast an object's motion changes (its acceleration, $a$)
depends on two things — how hard you push (the net force,
$F$) and how much "stuff" resists the change (the mass, $m$).
Bigger push → more acceleration. Bigger mass → less acceleration. Newton's
Second Law packs that into one tidy sentence:
Quick number: push a $2\text{ kg}$ cart with $10\text{ N}$ and it
accelerates at $a=10/2=5\text{ m/s}^2$ — every second it gains $5\text{ m/s}$.
Double the mass and the same push gives only half the acceleration.
Go deeper (AP / intro-college): vectors, momentum, and the Third Law
Force and acceleration are vectors — direction matters — so the
precise statement is $\sum\vec{F}=m\vec{a}$. Written through momentum
$\vec{p}=m\vec{v}$, it becomes the form Newton actually used,
$\vec{F}_{\text{net}}=\mathrm{d}\vec{p}/\mathrm{d}t$, which still works when
mass changes (rockets) or speeds get large. The Third Law
adds the partner idea: every push comes in a pair. When you push the wall, the
wall pushes back on you equally hard in the opposite direction
($\vec{F}_{AB}=-\vec{F}_{BA}$). The two forces act on different
objects, which is exactly why they don't cancel — and why a rocket flies by
throwing gas backward.
Try this in the simulation above
Switch to the ② F=ma mode and set friction $\mu=0$:
apply a force, then watch the block accelerate steadily and never stop — pure
First-Law motion once the force is removed. Now slide the Mass
up and re-launch with the same force: the acceleration readout drops in exact
proportion. Finally open ③ Action-Reaction and launch — the
two carts shoot apart with equal-and-opposite momentum, the Third Law made
visible.
Kinematics from 2nd Law. Integrating $a=F/m$ (constant $F$): $v(t)=v_0+at$, $x(t)=x_0+v_0 t+\tfrac{1}{2}at^2$. These are the SUVAT equations.
2
Atwood Machine. Two masses $m_1,m_2$ over a pulley: $a=\dfrac{(m_1-m_2)g}{m_1+m_2}$, Tension $T=\dfrac{2m_1 m_2 g}{m_1+m_2}$.
3
Inclined plane. Along slope: $ma=mg\sin\theta-\mu_k mg\cos\theta$. Normal force $N=mg\cos\theta$. Critical angle: $\tan\theta_c=\mu_s$.
4
Impulse–Momentum theorem. $\vec{J}=\int\vec{F}\,dt=\Delta\vec{p}=m\Delta\vec{v}$. A large force over a short time produces the same impulse as a small force over a long time.
5
Conservation of momentum. When $\vec{F}_{\text{net}}=0$, $\vec{p}_{\text{total}}=\text{const}$. Follows directly from 3rd Law: internal forces in a system cancel in pairs.
Ref: Halliday, Resnick & Walker — Fundamentals of Physics, 10th Ed., Ch. 5–6; Serway & Jewett — Physics for Scientists and Engineers, 8th Ed., Ch. 5–6; Kleppner & Kolenkow — An Introduction to Mechanics, 2nd Ed., Ch. 3.
Section 04
Frequently Asked Questions
① Inertia: an object slides freely or with friction, demonstrating the 1st Law. ② F=ma: apply a net force to a block and observe acceleration directly proportional to F and inversely proportional to m. ③ Action-Reaction: two carts push off each other, showing equal and opposite forces. ④ Atwood: two hanging masses over a pulley, demonstrating 2nd Law with gravity. ⑤ Incline: a block on a slope with adjustable friction and angle.
Gravity exerts a larger force on a heavier object, but that object also has more inertia (resistance to acceleration). The two effects cancel exactly: $a=F/m=mg/m=g$. This is Galileo's result confirmed by Newton's 2nd Law — all objects fall at the same rate $g$ regardless of mass (ignoring air resistance).
Car seatbelts rely on the 1st Law (inertia keeps you moving forward in a crash). Rocket propulsion uses the 3rd Law (exhaust gas pushes backward, rocket goes forward). Engineering structures use 2nd Law to calculate required forces. GPS satellites, planetary orbits, and all spacecraft trajectories are computed using Newton's laws.
Yes — always. The action and reaction forces are always equal in magnitude and opposite in direction, act on different objects, and are of the same type. They never cancel each other because they act on different bodies. A book on a table: the book pushes down on the table (gravity reaction), and the table pushes up on the book (normal force) — these are a 3rd-Law pair.
Mass ($m$) is inertia — resistance to acceleration — measured in kg. It is the same everywhere in the universe. Weight ($W=mg$) is the gravitational force on an object, measured in Newtons. On the Moon ($g=1.62$ m/s²) your mass is unchanged but your weight is ~6× less. The simulation's gravity slider changes $g$, affecting weight but not mass.
Newton's Laws are extremely accurate for everyday speeds and scales. They break down: (1) at speeds approaching $c$ (speed of light) — Special Relativity takes over; (2) at atomic/subatomic scales — Quantum Mechanics governs; (3) in very strong gravitational fields — General Relativity is needed. For all engineering and most physics problems, Newton's Laws are exact.
Resources: Khan Academy — Newton's Laws (khanacademy.org); HyperPhysics — Newton's Laws (hyperphysics.phy-astr.gsu.edu); MIT OCW 8.01 — Classical Mechanics.
Section 05
Common Misconceptions
❌ A moving object needs a constant force to keep moving.
✅ This is Aristotle's error, contradicted by Newton's 1st Law. Once moving, an object continues at constant velocity with zero net force. Friction is what slows objects in everyday life — it is a force, not the absence of force. In space (no friction), objects travel indefinitely without any propulsion.
📖 Halliday, Resnick & Walker, 10th Ed., §5-1; Arons — A Guide to Introductory Physics Teaching, Ch. 4.
❌ The action and reaction forces cancel each other out.
✅ Action-reaction forces act on different objects and therefore never cancel. A horse pulling a cart: the horse pulls the cart forward (action), the cart pulls the horse backward (reaction) — these are on different objects. Forces cancel only when they act on the same object with zero net result.
📖 Serway & Jewett, 8th Ed., §5-7: Newton's Third Law; Halliday et al., §5-4.
❌ Heavier objects fall faster than lighter ones.
✅ In a vacuum, all objects fall with the same acceleration $g$, regardless of mass. The gravitational force is proportional to mass, but so is inertia — they cancel in $a=F/m=mg/m=g$. Air resistance does make lighter/larger-surface objects fall slower in practice, but this is a separate force, not a property of gravity itself.
❌ If an object is at rest, there are no forces acting on it.
✅ An object at rest has zero net force, but may have many individual forces acting on it that balance. A book on a table has gravity pulling it down and the normal force pushing it up — two real forces that sum to zero. Zero net force means equilibrium, not the absence of forces.
📖 Halliday, Resnick & Walker, 10th Ed., §5-2: Force and Net Force.
❌ Inertia is a force that resists motion.
✅ Inertia is not a force — it is a property of mass. It describes an object's resistance to changes in its state of motion (whether at rest or moving). There is no "inertia force" in Newton's framework. Confusion arises because large inertia means a large force is needed to accelerate an object, but inertia itself does not push or pull anything.
📖 Kleppner & Kolenkow, 2nd Ed., §3.1; Arons — A Guide to Introductory Physics Teaching, Ch. 4.
Misconception research: Halloun & Hestenes (1985), Am. J. Phys. 53, 1043 — Force Concept Inventory; Arons — A Guide to Introductory Physics Teaching; Clement (1982), Am. J. Phys. 50, 66.