Physics terms in Space, time and motion

The rate of change of velocity, $a=\mathrm{\Delta }v\mathrm{/}\mathrm{\Delta }t$; a vector quantity measured in ${\text{m s}}^{-2}$.

The acceleration of a body falling under gravity alone, $g$; near the Earth's surface $g=9.8{\text{m s}}^{-2}$, directed downwards.

A graph of acceleration against time; the area between the line and the time axis is the change in velocity.

The rate of change of angular velocity, $\alpha =\mathrm{\Delta }\omega \mathrm{/}\mathrm{\Delta }t$, measured in ${\text{rad s}}^{-2}$.

The angle through which a body has turned about an axis, measured in radians, with a sense (clockwise or anticlockwise).

The product of a torque and the time for which it acts, $\tau \mathrm{\Delta }t$, equal to the change in angular momentum; the area under a torque–time graph.

The product of moment of inertia and angular velocity, $L=I\omega$ ($mvr$ for a particle), measured in ${\text{kg m}}^2{\text{s}}^{-1}$.

The angle swept out by the radius per unit time for a body moving in a circle, $\omega =2\pi \mathrm{/}T$, measured in ${\text{rad s}}^{-1}$; it is related to the speed by $v=\omega r$.

The force with which a support (such as bathroom scales) pushes up on a body; it differs from the true weight when the support accelerates vertically.

A body wholly or partly submerged in a fluid experiences an upward buoyancy force equal to the weight of the fluid it displaces, $F_{\mathrm{b}}=\rho Vg$.

The displacement of a body divided by the time taken, $\mathrm{\Delta }s\mathrm{/}\mathrm{\Delta }t$; on a displacement–time graph, the gradient of the chord between two times.

The line about which a body rotates; points on it do not move as the body turns.

The distance a vehicle travels from the moment the brakes are applied until it stops; for a constant deceleration it is proportional to the square of the initial speed.

The upward force of a fluid on a body in it, equal to the weight of fluid displaced: $F_{\mathrm{b}}=\rho Vg$.

The point at which the whole mass of a body can be treated as concentrated; the weight of a body acts through it.

The acceleration of a body moving in a circle, directed towards the centre: $a=v^2\mathrm{/}r={\omega }^{2}r$.

The resultant force on a body moving in a circle, directed towards the centre and perpendicular to the velocity: $F=m{v}^2\mathrm{/}r=m{\omega }^{2}r$. It is provided by real forces such as tension, friction or gravity.

The ratio of the friction force to the normal force for two surfaces: ${\mu }_{\mathrm{s}}$ for the maximum static friction, ${\mu }_{\mathrm{d}}$ while sliding. It has no unit.

One of two perpendicular vectors that together add up to a given vector; a vector $A$ at angle $\theta$ to the horizontal has components $A\cos \theta$ and $A\sin \theta$.

The total angular momentum of a system about an axis stays constant if no resultant external torque acts on it about that axis.

The total momentum of a system stays constant provided no resultant external force acts on it.

A force, such as gravity or an elastic force, whose work on a body moving between two points depends only on those points and not on the path taken.

A force that acts only while two bodies touch, such as the normal force, friction, tension, an elastic force, fluid resistance or buoyancy.

Two equal and opposite parallel forces whose lines of action are separated; it produces a torque $Fd$ about any axis but no resultant force.

A part of a vehicle designed to fold up in a controlled way in a collision, lengthening the stopping time and so reducing the average force on the occupants.

The change in position of a body, from its initial to its final position; a vector quantity measured in metres.

A graph of displacement (or position) against time; its gradient at any time is the velocity.

The spreading of energy into the surroundings, mostly as internal energy, in a form that can no longer do useful work.

The total length of the path travelled by a body; a scalar quantity measured in metres.

The forward force that propels a vehicle, exerted by the road on the driven tyres. At constant velocity it equals the total resistive force.

Friction between surfaces that are sliding over each other, $F_{\mathrm{f}}={\mu }_{\mathrm{d}}{F}_{\mathrm{N}}$; usually less than the maximum static friction.

The ratio of useful work (or power) output to total work (or power) input, $\eta$; it has no unit and can never exceed 1 (100 %).

A collision in which both momentum and the total kinetic energy of the bodies are conserved.

The energy stored in a body because it is deformed. For a spring obeying Hooke's law, $E_{\mathrm{H}}=\frac{1}{2}k\mathrm{\Delta }{x}^2$.

The capacity of a system to do work; a scalar quantity measured in joules (J) that is conserved in every process.

The energy released by a fuel per unit volume, measured in ${\text{J m}}^{-3}$.

The four equations linking $s$, $u$, $v$, $a$ and $t$ for a body moving in a straight line with uniform acceleration.

Something that happens at a single point in space at a single instant, described in a frame by one position and one time coordinate.

An interaction in which bodies fly apart from rest or from each other; momentum is conserved while kinetic energy increases at the expense of another store.

A force that acts across a distance without contact, even through a vacuum: gravitational, electric and magnetic forces.

The force exerted by a gas or liquid on a body moving through it, opposite to the body's velocity relative to the fluid; it increases with speed.

A heavy wheel with a large moment of inertia, used to store energy as rotational kinetic energy or to smooth out changes in rotation.

A push or a pull exerted by one body on another; a vector quantity measured in newtons (N).

Motion under the influence of gravity alone, with no other force (such as fluid resistance) acting.

A diagram of one body on its own showing every force that acts on it as a labelled arrow, with lengths roughly in proportion to the forces.

The component of the contact force parallel to two surfaces, which opposes their relative sliding or their tendency to slide.

A substance that releases energy in a controlled way, usually by burning or by nuclear reactions.

The principle that the laws of mechanics (Newton's laws) are the same in all inertial reference frames, with time the same for all observers.

The equations $x^{\mathrm{\prime }}=x-vt$ and $t^{\mathrm{\prime }}=t$ linking the coordinates of an event in two inertial frames in Newtonian physics, with velocities related by $u^{\mathrm{\prime }}=u-v$.

The gravitational force per unit mass at a point, in ${\text{N kg}}^{-1}$; $9.8{\text{N kg}}^{-1}$ near the Earth's surface.

The energy stored by a mass because of its position in a gravitational field. Near the Earth's surface its change is $\mathrm{\Delta }{E}_{\mathrm{p}}=mg\mathrm{\Delta }h$.

The elastic restoring force of a spring is proportional to its extension and opposite in direction, $F_{\mathrm{H}}=-kx$, up to the limit of proportionality.

The product of the average resultant force on a body and the time it acts, $J=F\mathrm{\Delta }t$; it equals the change in momentum and the area under a force–time graph.

A collision in which momentum is conserved but kinetic energy decreases; in a perfectly inelastic collision the bodies stick together.

The tendency of a body to resist changes to its velocity; the mass of a body is a measure of its inertia.

A reference frame that is not accelerating, in which a body with no resultant force on it stays at rest or moves with constant velocity.

The velocity of a body at one instant; on a displacement–time graph, the gradient of the tangent at that time.

The total of the random kinetic energies and intermolecular potential energies of the particles in a substance.

A quantity that has the same value in every inertial reference frame, such as the speed of light or the space-time interval.

A curve on a space-time diagram joining events with the same interval from the origin, used to mark equal units on the axes of different frames.

A system on which no resultant external force acts, so its total momentum stays constant.

The SI unit of work and energy: the work done when a force of 1 N moves its point of application 1 m in the direction of the force. $1\text{ J}=1\text{ N m}$.

A unit of energy: the energy transferred at a power of 1 kW for one hour, equal to $3.60\times {10}^6\text{ J}$.

The description of motion in terms of position, velocity and acceleration, without considering its causes.

The energy a body has because of its motion: $E_{\mathrm{k}}=\frac{1}{2}m{v}^2=p^2\mathrm{/}2m$.

The shortening of a moving object along its direction of motion: $L=L_0\mathrm{/}\gamma$, where $L_0$ is the proper length.

The region of a space-time diagram bounded by the 45° light lines through an event, containing all the events it can affect or be affected by.

The largest extension (or force) up to which the force on a spring or wire is proportional to its extension.

The straight line through the point where a force acts, in the direction of the force.

The product of the mass and the velocity of a body, $p=mv$; a vector measured in ${\text{kg m s}}^{-1}$ or N s.

$\gamma =1\mathrm{/}\sqrt{1-v^2\mathrm{/}{c}^2}$, the factor by which times are dilated and lengths contracted between frames moving at relative speed $v$; always at least 1.

The equations $x^{\mathrm{\prime }}=\gamma (x-vt)$ and $t^{\mathrm{\prime }}=\gamma (t-vx\mathrm{/}{c}^2)$ linking the coordinates of an event in two inertial frames in special relativity.

The mass of matter passing a point per unit time, $\mathrm{\Delta }m\mathrm{/}\mathrm{\Delta }t$, in ${\text{kg s}}^{-1}$; the force needed to change the velocity of a stream of matter by $\mathrm{\Delta }v$ is $(\mathrm{\Delta }m\mathrm{/}\mathrm{\Delta }t)\mathrm{\Delta }v$.

The sum of the kinetic, gravitational potential and elastic potential energy of a system. It is conserved when no friction or other resistive force does work.

An 1887 interferometer experiment that looked for a change in the speed of light with the direction of the Earth's motion and found none.

A measure of a body's resistance to angular acceleration about an axis, depending on how its mass is distributed about that axis; $I=\mathrm{\Sigma }m{r}^2$ for point masses, measured in ${\text{kg m}}^2$.

An unstable subatomic particle, like a heavy electron, with a mean lifetime of $2.2\mu \text{s}$ at rest; muons made by cosmic rays provide evidence for time dilation.

The SI unit of force: the resultant force that gives a mass of 1 kg an acceleration of $1{\text{m s}}^{-2}$, so $1\text{ N}=1{\text{kg m s}}^{-2}$.

A body stays at rest or moves with constant velocity in a straight line unless a resultant external force acts on it.

The resultant force on a body equals its rate of change of momentum, $F=\mathrm{\Delta }p\mathrm{/}\mathrm{\Delta }t$; for constant mass, $F=ma$.

The resultant torque on a rigid body equals its moment of inertia multiplied by its angular acceleration, $\tau =I\alpha$.

When body A exerts a force on body B, B exerts a force of the same type on A that is equal in size and opposite in direction.

A force, such as friction or fluid resistance, whose work depends on the path taken and which transfers mechanical energy to internal energy.

The component of the contact force between two surfaces that is perpendicular to them, $F_{\mathrm{N}}$.

In relativity, a reference frame with clocks at every position that records where and when each event happens, after allowing for the time light takes to arrive.

The fixed reference point from which positions are measured.

A collision in which the bodies stick together and move off with a common velocity; the loss of kinetic energy is the largest that momentum conservation allows.

The time for one complete cycle of a repeating motion, such as one revolution in circular motion, in seconds.

Where a body is relative to a chosen origin, given as a distance with a direction (or sign).

(1) The laws of physics are the same in all inertial reference frames; (2) the speed of light in a vacuum is the same for all inertial observers.

The rate of doing work or of transferring energy: $P=\mathrm{\Delta }W\mathrm{/}\mathrm{\Delta }t$, and $P=Fv$ for a force moving at velocity $v$. Measured in watts.

Energy cannot be created or destroyed, only transferred from one form or body to another, so the total energy of an isolated system is constant.

For a body in rotational equilibrium, the sum of the clockwise torques about any axis equals the sum of the anticlockwise torques about that axis.

A body that has been launched and then moves under gravity (and, in real cases, fluid resistance) with no other force acting.

The length of an object measured in the inertial frame in which it is at rest; the longest length any observer measures for it.

The time interval between two events measured in the inertial frame in which they happen at the same place; the shortest time any observer measures between them.

The angle at the centre of a circle subtended by an arc equal in length to the radius; a full circle is $2\pi$ rad.

The horizontal distance travelled by a projectile between its launch point and the point where it lands.

The time between a person seeing (or hearing) a signal and starting to respond to it, such as a driver seeing a hazard and pressing the brake.

A coordinate system, with an origin, axes and synchronised clocks, used to give the position and time of events.

The rule $u^{\mathrm{\prime }}=(u-v)\mathrm{/}(1-uv\mathrm{/}{c}^2)$ for the velocity of a body in a frame moving at $v$; it never gives a speed greater than $c$.

Two events at different places that are simultaneous in one inertial frame are not simultaneous in a frame moving along the line joining them.

The vector sum of all the forces acting on a body: the single force that would have the same effect as all of them together.

The sum of all the torques on a body about one axis, with clockwise and anticlockwise torques given opposite signs.

A unit of rotation rate used for machines; dividing by 60 gives revolutions per second, and multiplying by $2\pi \mathrm{/}60$ gives the angular velocity in ${\text{rad s}}^{-1}$.

An extended object whose shape and size do not change: the distance between any two of its points stays fixed.

Rolling in which the contact point has zero velocity relative to the surface, so the centre moves at $v=\omega r$.

Motion in which every point of a body moves in a circle about the same line, the axis of rotation.

The state of a body on which the resultant torque about any axis is zero, so its angular velocity does not change.

The kinetic energy a body has because it rotates, $E_{\mathrm{k}}=\frac{1}{2}I{\omega }^2=L^2\mathrm{/}2I$.

A diagram of energy transfers in which the width of each arrow is proportional to the energy or power it represents; useful output runs straight on and wasted energy branches away.

A quantity that has magnitude only, such as distance, speed, mass or time.

Space and time combined into one framework in which every event is a point, needed because the Lorentz transformation mixes position and time.

A graph of events with position $x$ on the horizontal axis and $ct$ on the vertical axis, on which light travels at 45°.

The quantity $\mathrm{\Delta }s$ given by $(\mathrm{\Delta }s{)}^2=(c\mathrm{\Delta }t{)}^2-(\mathrm{\Delta }x{)}^2$ for two events, which has the same value in every inertial frame.

A space-time interval with $(\mathrm{\Delta }s{)}^2<0$: not even light can link the events, so neither can cause the other and observers can disagree on their order.

Einstein's theory, based on two postulates, of how measurements of space and time made in different inertial reference frames are related.

The energy released by a fuel per unit mass, measured in ${\text{J kg}}^{-1}$.

The rate of change of distance travelled; a scalar quantity measured in ${\text{m s}}^{-1}$. It is the magnitude of the velocity.

The force per unit extension of a spring obeying Hooke's law, $k=F\mathrm{/}x$, measured in ${\text{N m}}^{-1}$; a stiffer spring has a larger $k$.

The state of a rigid body that is at rest with zero resultant force and zero resultant torque on it.

Friction between surfaces that are not sliding; it matches the applied force up to a maximum value, $F_{\mathrm{f}}\le {\mu }_{\mathrm{s}}{F}_{\mathrm{N}}$.

The viscous drag on a small sphere moving slowly through a fluid in laminar flow, $F_{\mathrm{d}}=6\pi \eta rv$, proportional to the radius, the speed and the viscosity.

The total distance a vehicle travels from the moment the driver sees a hazard until it stops: thinking distance plus braking distance.

The pulling force exerted by a stretched string, rope, cable or chain, acting along it and away from the body it is attached to.

The constant speed reached by a body falling through a fluid when the upward forces on it balance its weight, so that its acceleration is zero.

The distance a vehicle travels at constant speed during the driver's reaction time: speed × reaction time.

Two forces of the same type that two bodies exert on each other, equal in size and opposite in direction, acting on different bodies.

The forward force on a rocket or jet engine from expelling gas backwards, approximately the mass flow rate times the exhaust speed, $(\mathrm{\Delta }m\mathrm{/}\mathrm{\Delta }t)v$.

The lengthening of a time interval measured by an observer for whom a clock is moving: $\mathrm{\Delta }t=\gamma \mathrm{\Delta }{t}_0$, so a moving clock runs slow.

The total time a projectile spends in the air, from launch until it lands.

A space-time interval with $(\mathrm{\Delta }s{)}^2>0$: the events can be linked by a body slower than light, so one can cause the other and all observers agree on their order.

The turning effect of a force about an axis: the force multiplied by the perpendicular distance from the axis to its line of action, $\tau =Fr\sin \theta$, measured in $\text{N m}$.

The path followed by a moving body; for a projectile with no fluid resistance it is a parabola.

Motion in which every point of a body moves through the same displacement, without turning.

The state of a body on which the resultant force is zero, so that it is at rest or moves with constant velocity.

The kinetic energy of a body due to the motion of its centre of mass, $\frac{1}{2}m{v}^2$.

Acceleration that stays the same in magnitude and direction, so that the velocity changes by equal amounts in equal times.

Motion in a circle at constant speed; the velocity changes direction continuously, so the body accelerates towards the centre.

A quantity that has both magnitude and direction, such as displacement, velocity, acceleration or force.

The rate of change of displacement; a vector quantity measured in ${\text{m s}}^{-1}$.

A graph of velocity against time; its gradient is the acceleration and the area between the line and the time axis is the displacement.

A measure of how strongly a fluid resists flowing, symbol $\eta$, measured in Pa s.

The resistive force on a small sphere moving slowly through a fluid in laminar flow, given by Stokes' law $F_{\mathrm{d}}=6\pi \eta rv$; a special case of fluid resistance.

The SI unit of power: a rate of energy transfer of one joule per second.

The gravitational force on a body, $F_{\mathrm{g}}=mg$, measured in newtons and acting at its centre of mass.

The energy transferred when a force moves its point of application: $W=Fs\cos \theta$ for a constant force, where $\theta$ is the angle between the force and the displacement. Measured in joules.

The work done by the resultant force on a body equals the change in its kinetic energy.

The line on a space-time diagram joining all the events in a body's history; for constant velocity it is straight, at angle $\theta$ to the $ct$ axis with $\tan \theta =v\mathrm{/}c$.