What Physics Studies

Physics is divided into several major areas:

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.

Memory hook: Scalars are just a size (like a scale). Vectors have a direction (like an arrow pointing the way).

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.

Real-world examples:
  • 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)

Example: Find the force needed to accelerate a 5 kg box at 3 m/s²

F = m × a = 5 kg × 3 m/s² = 15 N

Example: Find the acceleration if a 1200 kg car has a net force of 3600 N applied to it

a = F / m = 3600 N / 1200 kg = 3 m/s²

Real-world intuition:
  • 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.

Real-world examples:
  • 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:

QuantityFormulaUnits
Speed / Velocityv = d / tm/s, km/h, mph
Distanced = v × tm, km, miles
Timet = d / vs, h
Example: A cyclist travels 120 km in 3 hours. What is her average speed?

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

Example: A car speeds up from 10 m/s to 34 m/s over 6 seconds. What is its acceleration?

a = (34 − 10) / 6 = 24 / 6 = 4 m/s²

Example: A ball decelerates from 20 m/s to 0 m/s in 4 seconds (braking). Find the deceleration.

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 / WeightW or FgPulls objects toward Earth's center; W = mg (g = 9.8 m/s²)
Normal ForceN or FNThe surface pushing back perpendicular to the contact surface
Frictionf or FfOpposes motion between surfaces; Ff = μN (where μ = friction coefficient)
Applied ForceFAA push or pull you apply to the object
TensionTForce transmitted through a rope, string, or cable
Example: Weight calculation

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)

Example: A worker pushes a box with 50 N of force across a floor 8 meters. How much work is done?

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

Example: A 2 kg ball moving at 6 m/s. Find its kinetic energy.

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)

Example: A 3 kg book rests on a shelf 2 meters high. What is its potential energy?

PE = mgh = 3 × 9.8 × 2 = 58.8 J

Formula Reference Table

ConceptFormulaUnits
Newton's Second LawF = maN (Newtons)
Speed / Velocityv = d / tm/s
Accelerationa = (vf − vi) / tm/s²
WeightW = mgN
WorkW = FdJ (Joules)
Kinetic EnergyKE = ½mv²J
Potential EnergyPE = mghJ

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

The trade-off with simple machines: Simple machines reduce the force needed, but they increase the distance over which that force must be applied. The total work done remains the same (in an ideal frictionless world). This is the law of conservation of energy at work.

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.