MATSEC IM Applied Mathematics key terms

A quantity that has size only, with no direction, such as mass, time or temperature. It is added and multiplied using ordinary arithmetic rules.

A quantity with both magnitude and direction, such as displacement, velocity or force. It is often written as a column of components or as a letter in bold type.

The size or length of a vector, ignoring its direction. For a two-dimensional vector with components a and b it equals the square root of a squared plus b squared.

One of the separate amounts of a vector along a chosen axis. A force can be split into horizontal and vertical components that act independently.

A vector of length one pointing in a given direction. Multiplying it by a scalar produces a vector of that length in the same direction.

The single vector that has the same effect as two or more vectors added together. It is found by vector addition, often using components or a triangle of vectors.

The state in which the total force and total moment acting on a body are both zero, so the body stays at rest or moves with constant velocity.

A measure of the turning effect of a force about a point, equal to the force multiplied by the perpendicular distance from the point to its line of action.

Two equal and opposite parallel forces whose lines of action do not coincide. They produce rotation but no net translational force on the body.

A contact force that opposes relative motion or the tendency to move between two surfaces. Its maximum value is usually proportional to the normal reaction.

The constant ratio between the limiting friction force and the normal reaction between two surfaces. It has no units and depends on the materials in contact.

The force exerted by a surface on a body pressing against it, acting perpendicular to the surface. On a horizontal floor it usually balances the weight.

An object moving freely under gravity alone after being launched. Its horizontal velocity stays constant while its vertical velocity changes at the acceleration due to gravity.

The path followed by a moving body through space. For a projectile without air resistance it is a parabola.

The constant downward acceleration experienced by a body in free fall near the Earth's surface, approximately 9.8 metres per second squared, denoted by g.

The gravitational force acting on a body, equal to its mass multiplied by the acceleration due to gravity. Unlike mass, it is a force measured in newtons.

A measure of the quantity of matter in a body, reflecting its resistance to acceleration. It is a scalar measured in kilograms and does not change with location.

The product of a body's mass and its velocity, a vector quantity measured in kilogram metres per second. It is conserved in collisions when no external force acts.

The product of a force and the time for which it acts, equal to the change in momentum it produces. It is measured in newton seconds.

The principle that the total momentum of a system stays constant when no external resultant force acts on it, as in collisions and explosions.

The energy transferred when a force moves a body through a distance in the direction of the force. It is measured in joules.

The energy a body possesses because of its motion, equal to half its mass times the square of its speed. It is a scalar measured in joules.

Energy stored in a body because of its position or condition, such as height above a reference level. Near the Earth it equals mass times g times height.

The principle that energy cannot be created or destroyed, only transferred or transformed between forms, so the total energy of an isolated system remains constant.

The rate at which work is done or energy is transferred, measured in watts. It equals work divided by time, or force multiplied by velocity.

The ratio of useful energy or power output to total energy or power input, often expressed as a percentage. It is always less than one in real machines.

The resultant force directed towards the centre of a circular path that keeps a body moving in that circle. It equals mass times speed squared divided by radius.

The rate of change of angle for a body moving in a circle, measured in radians per second. It equals the linear speed divided by the radius.

The angle subtended at the centre of a circle by an arc equal in length to the radius. One full turn equals two pi radians.

Oscillation in which the acceleration is proportional to the displacement from a fixed point and directed towards it. Its period does not depend on amplitude.

The maximum displacement of an oscillating body from its equilibrium position. It is measured in the same units as the displacement.

The time taken for one complete cycle of a repeating motion or wave. It is the reciprocal of frequency and is measured in seconds.

The number of complete cycles of a repeating motion or wave that occur each second. It is measured in hertz and equals one divided by the period.

A ratio of two sides of a right-angled triangle, such as sine, cosine or tangent, used to relate angles to lengths. These ratios are central to resolving vectors.

The process of splitting a single force into two perpendicular components that together have the same effect. It is used to analyse forces in different directions.

The calculus operation that finds the rate at which one quantity changes with respect to another, giving the gradient of a curve at a point.

The calculus operation that reverses differentiation, used to find a function from its rate of change or to calculate the area under a curve.

The value obtained by integrating a function between two limits, interpreted as the signed area under its graph between those limits. It gives a numerical result.

The slope of a line or curve at a point, equal to the change in the vertical quantity divided by the change in the horizontal quantity. It is found by differentiation for curves.

A straight line that touches a curve at a single point and has the same slope as the curve there. Its gradient equals the derivative at that point.