Physical Quantities, Units and Motion (Newton's Laws, Momentum, Friction)

Drafted with AI assistance and fact-checked on 28 October 2026; not yet read line by line by a human editor. Spotted a mistake? Tell us. Editorial standards & corrections

SI base and derived units

A physical quantity is anything that can be measured and expressed as a number with a unit. The International System of Units (SI), adopted in 1960, rests on 7 base quantities: length (metre), mass (kilogram), time (second), electric current (ampere), temperature (kelvin), amount of substance (mole) and luminous intensity (candela). All other units are derived from these: force in newton (1 N = 1 kg m/s^2), work and energy in joule (1 J = 1 N m), power in watt (1 W = 1 J/s) and pressure in pascal (1 Pa = 1 N/m^2). Exams often ask which unit in a list is not a base unit; newton, joule, watt and pascal are all derived. Tiny lengths use the angstrom (10^-10 m) and the nanometre (10^-9 m); astronomical distances use the light year (about 9.46 x 10^15 m), which is a distance and not a time, and the parsec (about 3.26 light years).

Scalars, vectors and displacement

A scalar has only magnitude (mass, time, distance, speed, work, energy, pressure); a vector has magnitude and direction (displacement, velocity, acceleration, force, weight, momentum). Electric current has a direction of flow but is a scalar because it does not add by the vector rule, a favourite trap. Distance is the total length of the path covered; displacement is the straight-line separation between the starting and finishing points, with direction. Distance is never less than displacement, and displacement can be zero when distance is not: an athlete who completes one lap of a circular track of radius r covers 2πr but ends with zero displacement, while after half a lap the displacement equals the diameter, 2r.

Speed, velocity and acceleration

Speed is distance divided by time; velocity is displacement divided by time, so velocity changes whenever the speed or the direction changes. Uniform circular motion, like that of a satellite in a circular orbit, is therefore accelerated motion even at constant speed. Acceleration is the rate of change of velocity (m/s^2); negative acceleration is called retardation. To convert, 1 km/h = 5/18 m/s, so 72 km/h = 20 m/s. A speedometer shows instantaneous speed and an odometer the distance covered. The slope of a distance-time graph gives speed, the slope of a velocity-time graph gives acceleration, and the area under a velocity-time graph gives displacement.

Equations of motion and free fall

For uniform acceleration, v = u + at, s = ut + (1/2)at^2 and v^2 = u^2 + 2as, where u is the initial velocity and v the final velocity. A freely falling body accelerates at g, about 9.8 m/s^2, so a stone dropped from rest moves at 19.6 m/s after 2 s. As Galileo argued, without air resistance heavy and light bodies fall together; in a tube emptied of air a feather and a coin land at the same moment.

Newton's three laws

Isaac Newton published his laws of motion in the Principia in 1687. The first law (law of inertia) says a body stays at rest or in uniform straight-line motion unless an unbalanced force acts on it; mass is the measure of inertia. Passengers lurch forward when a bus brakes suddenly and fall back when it starts suddenly, and dust leaves a carpet when it is beaten. The second law makes force equal to the rate of change of momentum, giving F = ma; 1 newton gives a mass of 1 kg an acceleration of 1 m/s^2. Force multiplied by time is impulse, equal to the change in momentum, so increasing the time of impact reduces the force: a fielder draws the hands back while catching, high jumpers land on foam or sand, and vehicles carry shock absorbers. The third law says every action has an equal and opposite reaction acting on a different body, so the pair never cancels; walking, swimming, a gun's recoil and rocket propulsion all show it.

Momentum and its conservation

Momentum is mass times velocity (p = mv), a vector measured in kg m/s. The law of conservation of momentum says the total momentum of a system stays constant when no external force acts on it. A gun and its bullet have zero momentum before firing; afterwards the light bullet flies forward fast and the heavy gun recoils slowly, so the total is still zero. A rocket throws hot gases backward and gains equal momentum forward, which is why it can accelerate even in empty space.

Friction

Friction opposes relative motion between surfaces in contact and arises from the interlocking of their tiny irregularities. Static friction is greater than sliding friction, which is greater than rolling friction, so wheels and ball bearings make movement easier. Friction wastes energy as heat and wears out shoe soles and machine parts, yet without it we could not walk, write, strike a match or stop a vehicle. Lubricants (oil, grease, graphite powder), polishing and ball bearings reduce it; treads on tyres and spikes on athletes' shoes increase grip. The friction of air and water is called drag, which is why birds, fish, boats and aircraft have streamlined shapes.

Key facts

SI has 7 base units: metre, kilogram, second, ampere, kelvin, mole and candela; newton, joule, watt and pascal are derived units.
A light year (about 9.46 x 10^15 m) measures distance, not time; 1 parsec is about 3.26 light years; 1 angstrom = 10^-10 m.
Scalars: mass, speed, distance, work, energy, pressure, electric current. Vectors: displacement, velocity, acceleration, force, weight, momentum.
One full lap of a circular track: distance = circumference, displacement = zero. Uniform circular motion is accelerated because the direction keeps changing.
1 km/h = 5/18 m/s, so 36 km/h = 10 m/s and 72 km/h = 20 m/s.
Equations of motion (uniform acceleration only): v = u + at; s = ut + (1/2)at^2; v^2 = u^2 + 2as. Free-fall acceleration g is about 9.8 m/s^2.
First law = inertia (passengers lurch forward when a bus brakes); second law F = ma (a fielder pulls the hands back to soften the catch); third law = equal and opposite reaction on a different body (rocket, gun recoil, swimming).
Momentum p = mv (kg m/s) is conserved when no external force acts: the basis of gun recoil and rocket propulsion.
Friction: static > sliding > rolling; ball bearings and lubricants reduce it, tyre treads and spiked shoes increase it; drag is friction in air and water.

Quick revision

SI (1960) has 7 base units: m, kg, s, A, K, mol, cd; newton, joule, watt, pascal are derived; light year measures distance; current is a scalar; displacement can be zero; 1 km/h = 5/18 m/s; v = u + at, s = ut + 1/2 at^2, v^2 = u^2 + 2as; g about 9.8 m/s^2; first law is inertia; F = ma; action and reaction act on different bodies; p = mv is conserved; static > sliding > rolling friction.

Practise this topic

All 12 lessons on General Science (Physics, Chemistry, Biology)