MATSEC IM Applied Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Constant acceleration equation set

The four standard equations linking u, v, a, s and t for uniform acceleration. Select the one that omits the quantity neither given nor required, then substitute consistent units.

Newton's second law

The resultant force on a particle equals its mass times acceleration, F = ma. Forces are resolved into components, and each direction gives a separate equation.

Limiting friction

When a body is on the point of sliding, friction reaches its maximum value F = μR, where μ is the coefficient of friction and R the normal reaction.

Normal reaction

The perpendicular contact force exerted by a surface on a body resting on it. On a horizontal surface it equals weight only if no other vertical forces act.

Resolving on an incline

With a slope at angle θ to the horizontal, the weight mg splits into mg sin θ along the slope and mg cos θ perpendicular to it.

Projectile independence of motions

Horizontal and vertical components of projectile motion are treated separately. Horizontal acceleration is zero; vertical acceleration is g directed downward throughout the flight.

Time of flight

For a projectile launched and landing at the same height, time of flight is 2u sin θ / g, obtained purely from the vertical component of velocity.

Range of a projectile

For launch and landing at equal heights, horizontal range is u² sin 2θ / g, which is greatest at a launch angle of 45 degrees.

Conservation of momentum

In any collision or explosion with no external resultant force, total momentum before equals total momentum after, summed as vectors over all bodies involved.

Coefficient of restitution

The ratio of relative speed of separation to relative speed of approach along the line of impact. It lies between zero and one.

Impulse

The product of a force and the time for which it acts, equal to the change in momentum produced. On a force–time graph it is the area under the curve.

Principle of moments

For a body in rotational equilibrium, the sum of clockwise moments about any point equals the sum of anticlockwise moments about that same point.

Couple

Two equal, opposite and parallel forces whose lines of action do not coincide. The moment of a couple is one force multiplied by the perpendicular separation.

Centre of mass

The point through which the weight of a body acts for all orientations. A freely suspended body rests with this point vertically below the suspension.

Triangle of forces

If three coplanar forces keep a particle in equilibrium they are concurrent and can be drawn head-to-tail as a closed triangle, solvable by sine and cosine rules.

Relative velocity

The velocity of A as observed from B, equal to the vector difference v_A minus v_B. Used to analyse interception and closest-approach problems.

Work done by a force

The product of force and displacement in the direction of the force, Fd cos θ. Work is measured in joules and may be negative.

Kinetic energy

The energy a body possesses due to motion, equal to half its mass times the square of its speed. It is a scalar and always non-negative.

Work–energy principle

The total work done by all forces on a body equals the change in its kinetic energy. Useful when forces vary or displacement is the unknown.

Power

The rate of doing work, measured in watts. When a driving force acts along the direction of motion, power equals force times speed.

Mechanical energy conservation

When only conservative forces do work, the sum of kinetic and potential energy stays constant. Friction converts mechanical energy into heat, so the sum falls.

Elastic modulus

For an elastic string or spring, tension equals the modulus times extension divided by natural length. The modulus has the dimensions of force.

Elastic potential energy

Energy stored in a stretched elastic string or spring, equal to modulus times extension squared divided by twice the natural length.

Hooke's law

The tension in an elastic string or spring is proportional to its extension, provided the elastic limit is not exceeded. The constant of proportionality depends on the material and dimensions.

Simple harmonic motion

Motion in which acceleration is proportional to displacement from a fixed point and directed toward it. Period is independent of amplitude.

Angular speed

The rate of change of angle for a body moving in a circle, equal to speed divided by radius. Measured in radians per second.

Centripetal acceleration

The acceleration of a body in circular motion, of magnitude v squared over r, directed toward the centre of the circle.

Centripetal force

The resultant inward force needed for circular motion, provided by real forces such as tension, friction or gravity, not an additional force.

Toppling condition

A body topples about an edge when the vertical line through its centre of mass falls outside the base, so the weight moment exceeds the restoring moment.

Differentiating displacement

Velocity is the derivative of displacement with respect to time, and acceleration is the derivative of velocity. Signs indicate direction along the chosen axis.

Integrating acceleration

Integrating acceleration gives velocity, and integrating again gives displacement. Each integration introduces a constant fixed by initial conditions.

Separable differential equation

A first-order equation in which variables can be grouped on opposite sides and integrated directly. The constant of integration is determined by a stated initial condition.