Glossary
Angle (theta)
The measure of the rotation between two intersecting lines or planes, often denoted by 'θ' and used to specify the direction of a vector relative to a reference axis.
Example:
The angle at which a projectile is launched significantly affects its trajectory and range.
Direction
The orientation or path along which a vector quantity points. It indicates 'which way' the quantity is acting.
Example:
When a bird flies north, 'north' specifies the direction of its flight.
Magnitude
The numerical value or size of a vector quantity, independent of its direction. It represents 'how much' of the quantity there is.
Example:
If a car is traveling at 60 mph, 60 mph is the magnitude of its velocity.
Pythagorean Theorem
A mathematical theorem stating that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides ($a^2 + b^2 = c^2$).
Example:
To find the length of the diagonal path across a rectangular field, you can use the Pythagorean Theorem with the field's length and width as the two sides.
Resolution into Components
The process of breaking down a single vector into its perpendicular x and y components using trigonometry. This simplifies analysis of forces or motion in multiple directions.
Example:
An engineer analyzing the forces on a bridge might use resolution into components to see how much of a diagonal tension force acts horizontally and vertically.
Resultant Vector
A single vector that represents the overall effect or sum of two or more individual vectors. It's the net outcome of combined vector quantities.
Example:
If you walk 3 meters east and then 4 meters north, your overall displacement from the start is the resultant vector of those two movements.
SOH CAH TOA
A mnemonic device used to remember the definitions of the sine (Opposite/Hypotenuse), cosine (Adjacent/Hypotenuse), and tangent (Opposite/Adjacent) trigonometric functions for a right triangle.
Example:
When trying to remember that sine is 'opposite over hypotenuse,' you can recall SOH CAH TOA.
Trigonometric Functions (Sine, Cosine, Tangent)
Mathematical functions (sin, cos, tan) that relate the angles of a right triangle to the ratios of its side lengths. They are essential for calculating vector components.
Example:
When calculating the height a ladder reaches against a wall, you'd use trigonometric functions like sine or cosine based on the ladder's length and angle.
Vector
A physical quantity that possesses both magnitude (size) and direction. It is often represented graphically as an arrow.
Example:
When a soccer player kicks a ball, the force applied is a vector because it has both a strength and a specific direction.
Vector Components
The perpendicular parts of a vector that represent its effect along specific axes, typically horizontal (x) and vertical (y).
Example:
A skateboarder pushing diagonally up a ramp has their force broken into horizontal and vertical vector components.