Glossary — Mechanics

Acceleration — the rate of change of velocity. Acceleration is a vector, so it has a direction as well as a magnitude.

Amplitude — the maximum displacement of an oscillation from its equilibrium position.

Angular frequency — the rate of change of the phase of an oscillation, $\omega = 2\pi f = \dfrac{2\pi}{T}$, measured in radians per second.

Angular velocity — the rate of change of angle for an object moving in a circle, $\omega = \dfrac{\Delta\theta}{\Delta t}$, measured in radians per second.

Centripetal acceleration — the acceleration of an object moving in a circle, directed towards the centre, with size $a = \dfrac{v^2}{r} = \omega^2 r$.

Centripetal force — the resultant force directed towards the centre of a circle that produces the centripetal acceleration, $F = \dfrac{mv^2}{r} = m\omega^2 r$. It is provided by a real force such as tension, friction or gravity.

Component — one of two perpendicular vectors that together have the same effect as a single vector. A vector $v$ at an angle $\theta$ to the $x$-axis has components $v\cos\theta$ along $x$ and $v\sin\theta$ along $y$.

Damping — the loss of energy from an oscillation to the surroundings, which makes the amplitude decay over time.

Displacement — the straight-line distance and direction from a start point to a finish point. Displacement is a vector.

Elastic collision — a collision in which both momentum and kinetic energy are conserved.

Equilibrium position — the position of an oscillating object when the resultant force on it is zero, and where it would rest.

Frequency — the number of complete oscillations per second, $f = \dfrac{1}{T}$, measured in hertz.

Free fall — motion under gravity alone, with air resistance taken as negligible.

Gravitational potential energy — the energy stored by an object because of its position in a gravitational field. Near the Earth, the change is $\Delta E_p = mg\Delta h$.

Impulse — the product of a force and the time for which it acts, $F\Delta t$. The impulse on an object equals its change in momentum.

Inelastic collision — a collision in which momentum is conserved but kinetic energy is not.

Inertia — the tendency of an object to keep its velocity. A larger mass has more inertia.

Kinetic energy — the energy an object has because of its motion, $E_k = \tfrac{1}{2}mv^2$.

Magnitude — the size of a vector, written without a direction. The magnitude of a velocity is a speed.

Momentum — the product of mass and velocity, $p = mv$. Momentum is a vector, measured in $\text{kg}\,\text{m}\,\text{s}^{-1}$.

Newton's first law — an object stays at rest, or keeps moving in a straight line at constant velocity, unless a resultant force acts on it.

Newton's second law — the resultant force on an object equals its mass multiplied by its acceleration, $F = ma$. In terms of momentum, $F = \dfrac{\Delta p}{\Delta t}$.

Newton's third law — if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. The two forces act on different objects.

Period — the time for one complete oscillation, $T = \dfrac{1}{f}$.

Power — the rate of transfer of energy, $P = \dfrac{W}{t} = Fv$, measured in watts.

Projectile — an object moving under gravity alone after it is launched, with air resistance taken as negligible.

Radian — the angle at the centre of a circle that cuts off an arc equal in length to the radius. A full circle is $2\pi$ radians, so $2\pi\ \text{rad} = 360^\circ$.

Resolving — replacing a vector by two perpendicular components that have the same combined effect.

Resultant — the single vector that has the same effect as two or more vectors added together.

Scalar — a quantity with a magnitude only, such as mass, time, temperature or energy.

Scale drawing — a drawing in which vectors are represented by arrows whose lengths are in a fixed proportion to their magnitudes. It adds vectors at any angle.

Simple harmonic motion — an oscillation in which the acceleration is proportional to the displacement from the equilibrium position and directed towards it, $a = -\omega^2 x$.

Terminal velocity — the constant velocity reached by an object falling through a fluid when the drag force equals its weight.

Triangle rule — the rule for adding two vectors: place the tail of the second at the tip of the first, and draw the resultant from the tail of the first to the tip of the second. A quantity is a vector only if it adds by this rule.

Vector — a quantity with a magnitude and a direction, such as displacement, velocity, acceleration or force.

Velocity — the rate of change of displacement. Velocity is a vector, so it has a direction as well as a magnitude.

Weight — the gravitational force on an object, $W = mg$. Weight is a vector, measured in newtons.

Work — the energy transferred when a force moves its point of application, $W = Fs\cos\theta$, measured in joules.