Physics Basics
Physics is the science of matter, energy, and the forces that govern how they interact. It explains why a ball falls when you drop it, why a car skids on ice, and how a lever lets you lift something heavier than you could on your own. This guide covers the essential physics concepts taught in middle and high school: scalars and vectors, Newton's three laws of motion, kinematics formulas, forces, work and energy, and simple machines.
What Physics Studies
Physics is divided into several major areas:
- Mechanics: How objects move and what causes motion (forces, acceleration, momentum)
- Thermodynamics: Heat, temperature, and energy transfer
- Waves and Sound: How energy travels through vibrations
- Optics: The behavior of light
- Electricity and Magnetism: Electric charge, circuits, and magnetic fields
This guide focuses on mechanics — the area most commonly covered in introductory physics courses.
Scalar vs. Vector Quantities
Before working with physics formulas, you need to understand the difference between two types of measurements.
| Type | Definition | Examples |
|---|---|---|
| Scalar | Has magnitude (size) only | speed, distance, mass, temperature, time |
| Vector | Has both magnitude and direction | velocity, displacement, force, acceleration |
The distinction matters because direction changes the math. A car driving 60 km/h north and a car driving 60 km/h south are traveling at the same speed (scalar) but opposite velocities (vectors). If they collide head-on, the forces do not cancel out — they compound.
Newton's Three Laws of Motion
Sir Isaac Newton published his three laws of motion in 1687. These laws describe how forces cause objects to move (or stay still) and are the foundation of classical mechanics.
First Law: The Law of Inertia
"An object at rest stays at rest, and an object in motion stays in motion at the same speed and in the same direction, unless acted on by an unbalanced external force."
What it means: Objects do not change what they are doing on their own. You have to push or pull something to get it to change. The tendency of an object to resist changes in motion is called inertia. Objects with more mass have more inertia.
- A hockey puck sliding across ice keeps moving because there is very little friction to slow it down.
- When a car stops suddenly, passengers lurch forward because their bodies want to keep moving.
- A tablecloth can be pulled out from under dishes quickly because the dishes have inertia and resist moving.
Second Law: The Law of Acceleration
"The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass."
This law gives us the most important formula in classical mechanics:
F = ma
Where F = net force (in Newtons, N), m = mass (in kilograms, kg), a = acceleration (in meters per second squared, m/s²)
F = m × a = 5 kg × 3 m/s² = 15 N
a = F / m = 3600 N / 1200 kg = 3 m/s²
- The same force accelerates a small car faster than a large truck (less mass = more acceleration).
- To accelerate a loaded shopping cart, you need more force than for an empty one.
Third Law: The Law of Action-Reaction
"For every action, there is an equal and opposite reaction."
When object A exerts a force on object B, object B exerts an equal force in the opposite direction on object A. Forces always come in pairs.
- You push off the wall of a pool; the wall pushes you backward into the water.
- A rocket fires gas downward; the gas pushes the rocket upward.
- A gun fires a bullet forward; the gun recoils (kicks) backward with equal momentum.
- Walking works because your foot pushes the ground backward; the ground pushes you forward.
Speed, Velocity, and Acceleration
Speed and Velocity
Speed is how fast an object is moving (scalar). Velocity is speed in a specific direction (vector). Both use the same formula:
| Quantity | Formula | Units |
|---|---|---|
| Speed / Velocity | v = d / t | m/s, km/h, mph |
| Distance | d = v × t | m, km, miles |
| Time | t = d / v | s, h |
v = d / t = 120 km / 3 h = 40 km/h
Acceleration
Acceleration is the rate at which velocity changes over time. It is a vector quantity — an object accelerates when it speeds up, slows down, or changes direction.
a = (vf − vi) / t
Where vf = final velocity, vi = initial velocity, t = time elapsed
a = (34 − 10) / 6 = 24 / 6 = 4 m/s²
a = (0 − 20) / 4 = −20 / 4 = −5 m/s²
The negative sign indicates deceleration (slowing down).
Forces
A force is a push or pull on an object. Forces are vectors, measured in Newtons (N). The net force is the vector sum of all forces acting on an object.
FORCE DIAGRAM (Free Body Diagram) for a book on a table:
Normal Force (N) [up]
^
|
____________|____________
| | <-- book
|_________________________|
|
v
Weight / Gravity (W) [down]
Net Force = N - W = 0 (book is at rest, forces are balanced)
Common Types of Forces
| Force | Symbol | Description |
|---|---|---|
| Gravity / Weight | W or Fg | Pulls objects toward Earth's center; W = mg (g = 9.8 m/s²) |
| Normal Force | N or FN | The surface pushing back perpendicular to the contact surface |
| Friction | f or Ff | Opposes motion between surfaces; Ff = μN (where μ = friction coefficient) |
| Applied Force | FA | A push or pull you apply to the object |
| Tension | T | Force transmitted through a rope, string, or cable |
What is the weight of a 70 kg person on Earth?
W = mg = 70 kg × 9.8 m/s² = 686 N
Work and Energy
Work
In physics, "work" has a specific meaning: it is done when a force moves an object through a distance in the direction of the force. If the force does not move the object, no work is done (in the physics sense).
W = F × d
Where W = work (in Joules, J), F = force (in Newtons, N), d = distance moved in direction of force (in meters, m)
W = F × d = 50 N × 8 m = 400 J
Kinetic Energy
Kinetic energy (KE) is the energy an object has because of its motion.
KE = ½mv²
KE = ½ × 2 × 6² = ½ × 2 × 36 = 36 J
Gravitational Potential Energy
Potential energy (PE) is stored energy due to position. Gravitational PE depends on an object's height above a reference point.
PE = mgh
Where m = mass (kg), g = 9.8 m/s², h = height (m)
PE = mgh = 3 × 9.8 × 2 = 58.8 J
Formula Reference Table
| Concept | Formula | Units |
|---|---|---|
| Newton's Second Law | F = ma | N (Newtons) |
| Speed / Velocity | v = d / t | m/s |
| Acceleration | a = (vf − vi) / t | m/s² |
| Weight | W = mg | N |
| Work | W = Fd | J (Joules) |
| Kinetic Energy | KE = ½mv² | J |
| Potential Energy | PE = mgh | J |
Simple Machines
A simple machine is a device that changes the direction or magnitude of a force to make work easier. They do not reduce the amount of work done overall, but they let you use less force over a greater distance (or change the direction of the force).
Lever
A lever is a rigid bar that pivots around a fixed point called the fulcrum. By placing the fulcrum closer to the load (heavy object), a small force applied over a long distance can lift the load.
Effort Load
| |
v v
============================
^
Fulcrum
The closer the fulcrum to the load, the less effort needed.
Examples: seesaw, crowbar, scissors, bottle opener
Pulley
A pulley is a wheel with a rope over it. A single fixed pulley changes only the direction of the force (you pull down to lift up). Adding more pulleys (compound pulley) reduces the effort needed.
Examples: flagpole, window blinds, cranes, elevators
Inclined Plane
An inclined plane (ramp) allows you to move a heavy object to a greater height by pushing it along a longer, gentler slope. Less force is needed, but over a greater distance.
Examples: wheelchair ramps, loading docks, roads up a mountain
Wheel and Axle
A wheel and axle consists of a large wheel attached to a smaller cylinder (axle). Turning the large wheel with a small force creates a larger force at the axle.
Examples: steering wheel, doorknob, screwdriver, gear systems
Frequently Asked Questions
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms (kg). It does not change regardless of where you are in the universe. Weight is the gravitational force acting on that mass, measured in Newtons (N). Weight changes depending on gravity. On the Moon, where gravity is about 1/6 of Earth's, a person with a mass of 70 kg would still have a mass of 70 kg, but their weight would be about 114 N instead of 686 N. Scales on Earth display weight in kilograms for convenience, but technically they measure force.
What does it mean when the net force is zero?
When the net force on an object is zero, the object is in a state called equilibrium. By Newton's First Law, this means it will not change its motion. If it was at rest, it stays at rest. If it was moving, it continues moving at constant speed in the same direction. An example is a book sitting on a table: gravity pulls it down with 9.8 N per kilogram of mass, and the table's normal force pushes back up with the same magnitude. Net force = 0, so the book does not accelerate.
Why does a feather fall more slowly than a rock?
In a vacuum (no air), a feather and a rock actually fall at exactly the same rate. This was famously demonstrated by dropping a hammer and a feather on the Moon (no atmosphere) and seeing them hit the ground simultaneously. On Earth, air resistance is the difference. Air resistance is a force that opposes motion through air. It depends on the shape and surface area of an object. A feather has a large surface area relative to its weight, so air resistance has a much greater effect on it than on a dense, compact rock. In the absence of air, gravity accelerates all objects equally: 9.8 m/s².
What is momentum and how is it related to Newton's laws?
Momentum (p) is the product of an object's mass and its velocity: p = mv, measured in kg·m/s. It describes how hard it is to stop a moving object. Newton's Second Law can actually be stated as: force equals the rate of change of momentum (F = Δp / t), which is the more general form. The Law of Conservation of Momentum states that in a closed system with no external forces, the total momentum before a collision equals the total momentum after. This explains why a large, slow-moving truck can cause more damage than a small, fast-moving car — the truck has much more momentum because of its greater mass.
Quick Quiz
Check your understanding. Click an answer to see if you got it right.