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Physical quantity
A measurable property expressed with a magnitude and a unit.
Base quantity
A fundamental physical quantity defined and measured independently of other quantities.
Derived quantity
A physical quantity calculated from base quantities using mathematical operations.
Scalar quantity
A quantity that has magnitude only.
Vector quantity
A quantity that has both magnitude and direction.
Systematic error
A measurement error that consistently skews readings in the same direction by a fixed amount.
Zero error
A systematic error that occurs when an instrument does not read exactly zero when it should.
Parallax error
A systematic error caused by improper eye position when reading a scale.
Random error
A measurement error that varies unpredictably in magnitude and direction from trial to trial.
Precision
Closeness of repeated measurements to one another under unchanged conditions.
Accuracy
Closeness of a measured value to the true or accepted value.
Uncertainty (Δ)
The range within which the true value of a measurement is expected to lie.
Homogeneity of equations
The requirement that every term in a physical equation has the same dimensions.
Dimensionless constant
A constant with no units.
Distance (d)
Total length covered by a moving object regardless of direction.
Displacement (s)
Straight-line distance of an object from a reference point with direction.
Speed |v|
Rate of change of distance with time.
Velocity (v)
Rate of change of displacement with time.
Acceleration (a)
Rate of change of velocity with time.
Uniform acceleration
Constant acceleration over time.
Free fall
Motion under gravity alone with no other forces acting.
Terminal velocity
Constant maximum velocity when drag equals weight.
Rectilinear motion
One-dimensional motion along a straight line.
Newton’s first law
A body remains at rest or in uniform straight-line motion unless acted on by a resultant external force.
Inertia
Resistance of a mass to changes in its state of motion.
Newton’s second law
Rate of change of momentum equals the net force acting; for constant mass, F = ma.
Newton’s third law
For every action force there is an equal and opposite reaction force.
Linear momentum (p)
Product of mass and velocity (p = mv).
Impulse (J)
Product of average force and time of impact; equals change in momentum.
Principle of conservation of momentum
Total momentum of a closed system remains constant in absence of external forces.
Elastic collision
Collision conserving both momentum and kinetic energy.
Inelastic collision
Collision conserving momentum but not kinetic energy.
Perfectly inelastic collision
Collision where objects stick together, losing maximum kinetic energy.
Field of force
Region where objects with certain properties experience a force.
Stability (mechanics)
Ability of an object to return to equilibrium after displacement.
Static equilibrium
State of rest with zero resultant force and torque.
Translational equilibrium
Motion with constant velocity and zero resultant force.
Rotational equilibrium
Zero angular acceleration; resultant torque is zero.
Force
Rate of change of momentum with time; an interaction that changes motion.
Gravitational force FG
Attractive force exerted by Earth (or masses) on objects with mass.
Electrostatic force FE
Attractive or repulsive force between electric charges.
Magnetic force FM
Attractive or repulsive force between magnets or moving charges.
Friction (f)
Force opposing motion between contacting surfaces.
Viscous (drag) force
Resistive force due to a fluid’s viscosity acting on an object moving through it.
Air resistance
Drag force exerted by air on moving objects.
Normal contact force (N)
Perpendicular push exerted by a surface on an object.
Tension (T)
Pull transmitted by a stretched string, rope or spring.
Mass (m)
Measure of the amount of matter in a body.
Weight (W)
Gravitational force on a mass; W = mg.
Apparent weight
Perceived weight modified by system acceleration.
Component forces
Projections of a force along perpendicular axes (Fx = F cosθ, Fy = F sinθ).
Hooke’s law
Extension/compression of a spring is proportional to applied force, F = kx, within elastic limit.
Spring constant (k)
Measure of a spring’s stiffness.
Centre of gravity
Imaginary point where the total weight of an object acts.
Moment of a force (M)
Product of force and perpendicular distance from pivot (M = Fd⊥).
Torque of a couple (τ)
Rotational effect of two equal, opposite forces with separated lines of action; τ = Fd⊥.
Principle of moments
For equilibrium, total clockwise moments equal total anticlockwise moments about any pivot.
Density (ρ)
Mass per unit volume (ρ = m/V).
Pressure (P)
Force per unit area (P = F/A).
Hydrostatic pressure
Pressure in a fluid at rest due to gravity (P = hρg).
Upthrust (U)
Upward force on a submerged object due to pressure difference; U = Vρg.
Archimedes’ principle
Upthrust on a body equals the weight of fluid displaced.
Principle of floatation
A floating object experiences upthrust equal to its weight.
Work done (W)
Product of force and displacement in force direction; for gases, W = pΔV.
Energy
Capacity to do work.
Conservation of energy
Energy cannot be created or destroyed, only transformed or transferred.
Kinetic energy (KE)
Energy due to motion: KE = ½ mv².
Gravitational potential energy (GPE)
Energy due to position in gravitational field: GPE = mgh (near Earth’s surface).
Electric potential energy
Energy of a charge due to its position in an electric field.
Elastic potential energy (EPE)
Energy stored when an object is stretched/compressed: EPE = ½ kx².
Power (P)
Work done per unit time; P = W/t or P = Fv.
Efficiency (η)
Useful output energy or power divided by input energy or power, expressed as a percentage.
Angular displacement (θ)
Angle subtended at circle centre by an arc (θ = s/r).
Angular velocity (ω)
Rate of change of angular displacement (ω = dθ/dt = 2πf).
Period (T)
Time for one complete revolution or oscillation.
Frequency (f)
Number of revolutions or oscillations per unit time (f = 1/T).
Linear speed (v)
Speed along circular path: v = rω.
Centripetal acceleration (ac)
Acceleration toward circle centre: ac = v²/r = rω².
Centripetal force
Net inward force needed for circular motion: F = mv²/r.
Centrifugal force
Apparent outward force observed in a rotating frame.
Helical motion
Spiral path combining rotation about and translation along an axis.
Newton’s law of gravitation
Force between masses: FG = GMm/r².
Gravitational field
Region where a mass experiences gravitational force.
Gravitational field strength (g)
Force per unit mass at a point: g = FG/m.
Gravitational potential energy (U)
Work done to bring mass from infinity: U = –GMm/r.
Gravitational potential (φ)
Work done per unit mass to bring mass from infinity: φ = –GM/r.
Geostationary orbit
Equatorial orbit with 24-h period, remaining fixed above a point on Earth.
Escape velocity (ve)
Minimum speed to leave Earth’s gravitational field: ve = √(2GM/r).
Equipotential lines (gravity)
Surfaces where gravitational potential is constant.
Kepler’s third law
Square of orbital period is proportional to cube of orbit radius (T² ∝ r³).
Kelvin (K)
SI unit of temperature measured from absolute zero.
Thermal equilibrium
State where bodies share the same temperature; no net energy flow.
Ideal gas
Hypothetical gas obeying pV = nRT with negligible particle volume and no intermolecular forces.
Ideal-gas assumptions
Random motion, negligible particle volume, negligible forces except in elastic collisions, brief collisions.
Mean translational KE (gas)
Average KE per molecule: ½ m⟨c²⟩ = 3/2 kT.
Boyle’s law
For fixed T, gas pressure is inversely proportional to volume (p ∝ 1/V).
Charles’ law
For fixed p, gas volume is directly proportional to temperature (V ∝ T).
Gay-Lussac’s law
For fixed V, gas pressure is proportional to temperature (p ∝ T).
Internal energy (U)
Sum of microscopic kinetic and potential energies of molecules in a system.
Zeroth law of thermodynamics
If A is in thermal equilibrium with B and with C, then B is in thermal equilibrium with C.