Coordinate Systems and Trigonometry

This set of flashcards covers key concepts related to coordinate systems and trigonometry, including definitions and formulas associated with motion, forces, and kinematic equations.

Velocity

The rate of change of position; calculated as change in position divided by time elapsed, represented as extbf{v} = \frac{\Delta \textbf{x}}{\Delta t}.

Displacement

The change in position of an object, calculated as final position minus initial position, expressed as \Delta \textbf{x} = x_f - x_i.

Acceleration

The rate of change of velocity, defined as change in velocity divided by time elapsed, represented as a = \frac{\Delta v}{\Delta t}.

Kinematic Equations

Formulas that relate the five main variables of motion: displacement, initial velocity, final velocity, acceleration, and time.

Gravitational Force

The force of attraction between two masses, represented as F_g = \frac{G m_1 m_2}{r^2}, where G is the gravitational constant.

Static Friction

The force that resists the initiation of sliding motion between two surfaces in contact, represented as f_s \leq \mu_s n.

Average Velocity

The total displacement divided by the total time taken, a vector quantity.

Momentum

A measure of the motion of an object, calculated as the product of its mass and velocity, represented as p = mv.

Newton’s First Law

An object will remain at rest or in uniform motion unless acted upon by a net external force.

Newton’s Second Law

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as \Sigma F = ma.

Free-Body Diagram

A graphical representation used to visualize the forces acting on an object, showing all forces as vectors.

Instantaneous Velocity

The speed and direction of an object at a specific moment in time; the slope of the tangent line on a position vs. time graph.

Force

A vector quantity that represents a push or pull on an object, which can cause it to accelerate.

Unit Conversion

The process of converting a quantity from one unit of measurement to another, using known equivalences.

Contact Forces

Forces that occur when two objects are in physical contact with each other.

Field Forces

Forces that act at a distance, such as gravitational or electromagnetic forces.

Net Force

The vector sum of all forces acting on an object, determining its acceleration.

Kinetic Friction

The force that opposes the motion of two surfaces sliding past each other, represented as f_k = \mu_k n.