Topic Cluster

Classical Mechanics

Classical mechanics: forces, energy, momentum and motion — Newton’s laws, work and energy, collisions, rotation and the everyday mechanics the rest of physics is built on.

Classical Mechanics — the core equations of classical mechanics, and every article on the topic
The equations this topic keeps coming back to.

What Is Classical Mechanics?

Classical Mechanics is the physics of why motion changes: the forces, energy and momentum that govern everything from a rolling ball to an orbiting satellite. Everything else in physics leans on it.

Core equations in classical mechanics
RelationshipEquationWhat it tells you
Newton's second lawF = m·aNet force, mass and acceleration
Work doneW = F·d·cosθEnergy transferred by a force
Kinetic energyKE = ½·m·v²Energy of a moving mass
Gravitational PEPE = m·g·hEnergy stored by height
Momentump = m·vConserved in every collision
Torqueτ = r·F·sinθTurning effect of a force
Significant Figures in Physics
Classical Mechanics

Significant Figures in Physics

Significant figures are the digits of a measurement that its own resolution supports, and there are two rules rather than one: multiplying keeps the fewer figure count, while adding keeps the coarser decimal place - which is how 1.0 plus 9.999 comes out as 11.0, three figures from a two-figure reading. The half most explanations skip is what a count is worth. Three figures on 1.00 claims 0.5000 per cent while three figures on 9.99 claims 0.05005 per cent, a factor of 9.99 apart, so multiplying 1.00 by 9.99 leaves the rule quoting three figures where the two readings support one. This page counts all four zero cases, states both rules, prices the digits as a percentage, shows where subtraction destroys them, and works eight problems step by step.

22 min read
Efficiency in Physics
Classical Mechanics

Efficiency in Physics

Efficiency is one division: the useful output over the total input, times 100 for a percentage. The ratio carries no unit, so joules over joules and watts over watts give the same answer, and the time interval cancels exactly rather than nearly. The half that most explanations skip is what happens when stages run in series. Stage efficiencies multiply, so four stages given as 38, 96, 92 and 88 per cent come out at 29.53 per cent overall - below the worst of the four, and nowhere near their average. This page works the division in all three directions, shows why adding and averaging a chain are both wrong, measures what rounding a stage too early costs, and works eight problems step by step, from a lamp to a four-stage chain that loses 704657.92 J of every megajoule it is given.

18 min read
Dimensional Analysis in Physics
Classical Mechanics

Dimensional Analysis in Physics

Every mechanical quantity is a triple of exponents over mass, length and time, and that triple is all dimensional analysis ever works with: multiplying quantities adds the triples, raising one to a power scales them, and an equation is only admissible when both sides match row for row. The half most explanations skip is how far that gets you. Three base dimensions give three equations, so three ingredients pin down the exponents of a law exactly - a pendulum period comes out as T = k L^0.50 g^-0.50 with the mass gone entirely - while the constant k in front stays out of reach for ever. This page works the exponent algebra, derives two laws from scratch, shows the 1/2 m v^2 case that passes the check at four times the right answer, scales a quantity with no constant at all, and works eight problems step by step, including the one where no exponents balance and that is the useful result.

24 min read
Newton’s Third Law: Examples
Classical Mechanics

Newton’s Third Law: Examples

Newton's third law says that when two bodies interact, each pushes on the other with the same size of force in the opposite direction, written F_12 = -F_21. The half most people drop is the half that matters: the two forces act on different bodies, one on each, so they never cancel and the two accelerations they produce are almost never equal. This page fixes the on X by Y convention, gives a three-condition test for spotting a genuine pair, names both bodies in seven everyday examples, proves that a book's weight and the table's push are not a pair by putting the book in a lift, resolves the tug of war and the horse and cart, and works eight problems step by step - including the two-block case where the same push and the same acceleration give an internal force of 9.000 N or 15.00 N depending on which end you push.

24 min read
Orbital Velocity: Formula and Worked Examples
Classical Mechanics

Orbital Velocity: Formula and Worked Examples

Orbital velocity is the speed a body needs to hold a circular orbit at a given radius, and gravity alone fixes it: v = sqrt(GM/r), with the radius measured from the centre of the body and not from its surface. The consequence catches almost everyone out. Because the speed goes as one over the square root of the radius, four times the radius is exactly half the speed, so a higher orbit is a slower orbit. This page sets out the force-balance derivation, the symbol table, a seven-row ladder of real orbits from a surface skim to the Moon with speed, period and local gravity side by side, how much gravity there really is at the space station, where the circular model breaks down, and eight problems worked step by step.

22 min read
Geostationary Orbit Explained
Classical Mechanics

Geostationary Orbit Explained

A geostationary orbit is the single circular orbit, 35,786 km above the equator, in which a satellite's period matches one sidereal day - so it hangs over one spot and a dish aimed at it never has to move. This page gives the three conditions that define it, the one altitude that follows, and the thing the usual shorthand gets wrong: the period is 23 hours 56 minutes 4 seconds, not 24 hours, and a satellite built to 24 hours drifts almost a degree west every day until it has lapped the globe. Seven worked problems, two original diagrams and an interactive ground-track lab.

20 min read
Escape Velocity Explained: Formula, Five Worlds and Worked Examples
Classical Mechanics

Escape Velocity Explained: Formula, Five Worlds and Worked Examples

Escape velocity is the launch speed at which an unpowered object leaves a world for good: 11.18 km/s at Earth's surface, 2.375 km/s at the Moon's and 617.8 km/s at the Sun's. This page derives v = sqrt(2GM/r) from energy conservation, puts five worlds side by side against NASA's own published figures, shows why half the escape speed lifts a projectile only one third of a radius, and explains why no rocket ever has to reach 11.2 km/s. Seven worked problems, two original diagrams, an interactive lab and a calculator.

19 min read