Physics Vectors and Scalars

Vocabulary flashcards covering scalar and vector quantities, vector addition methods, resultant vectors, scale diagrams, and vector resolution.

Scalar Quantity

A quantity that has magnitude only (where magnitude means size or amount) and is completely described by a numerical value and unit, such as distance, speed, mass, time, temperature, energy, and density.

Vector Quantity

A quantity that has both magnitude and direction, such as displacement, velocity, acceleration, and force, which cannot be completely described by magnitude alone.

Vector Representation

A graphical representation of a vector using an arrow, where the length of the arrow represents magnitude according to a chosen scale, and the arrowhead shows direction.

Scale Diagram

An accurate drawing used to represent vectors where a stated scale is used, requiring a ruler for measuring lengths and a protractor for measuring angles or directions.

Head-to-Tail Method

A graphical method to add vectors by drawing the first vector, drawing the second vector starting at the head of the first, and drawing the resultant vector from the tail of the first vector to the head of the final vector.

Resultant Vector

A single vector that has the overall effect of two or more vectors acting together, possessing both magnitude and direction.

Vectors in the Same Direction

Vectors acting along the same straight line in the same direction whose magnitudes are added together to determine the resultant (for example, $6\,\text{N}$ east plus $4\,\text{N}$ east equals $10\,\text{N}$ east).

Vectors in Opposite Directions

Vectors acting along a straight line in opposite directions, where the smaller magnitude is subtracted from the larger magnitude and the resultant acts in the direction of the larger vector (for example, $12\,\text{N}$ east and $7\,\text{N}$ west give a resultant of $5\,\text{N}$ east).

Perpendicular Vectors

Two vectors acting at $90^\circ$ that form the two shorter sides of a right-angled triangle, where the resultant is the diagonal whose magnitude can be calculated using $R^2 = A + B^2$.

Resolving Vectors

The process of replacing one vector with two or more component vectors (commonly perpendicular horizontal and vertical components in CSEC problems) that together have the same effect.

Component Vectors

Perpendicular vector parts that allow a motion or force to be analyzed separately in perpendicular directions, which is useful when studying forces on slopes, projectile motion, or unaligned axes.

Vector Answer Checking

The practice of ensuring vector answers include the correct unit and direction, verifying that perpendicular vectors yield a resultant longer than either component vector but shorter than their arithmetic sum.

Scalar Quantity

A quantity that has magnitude only, where magnitude means size or amount, and is completely described by a numerical value and unit.

Vector Quantity

A quantity that has both magnitude and direction, which cannot be completely described by writing only its magnitude.

Arrow Representation of a Vector

A graphical symbol where the length of the arrow represents magnitude according to a chosen scale, and the arrowhead shows direction.

Scale Diagram

An accurate drawing used to represent vectors that must state a scale and requires a ruler for length and a protractor for angles or directions.

Head-to-Tail Method

A graphical method to add vectors by drawing the second vector starting at the head of the first vector, with the resultant drawn from the tail of the first vector to the head of the final vector.

Resultant Vector

A single vector that has the overall effect of two or more vectors acting together, which must have both magnitude and direction.

Perpendicular Vectors

Vectors acting at $90^\text{o}$, forming the two shorter sides of a right-angle triangle whose resultant diagonal magnitude can be calculated using $R^2 = A + B^2$.

Resolving Vectors

The process of replacing one vector with two or more component vectors that together have the same effect.

Vector Components

Perpendicular component vectors that allow a motion or force to be analyzed separately in perpendicular directions, such as studying forces on slopes or projectile motion.

Vectors in the Same Direction

Vectors acting along the same straight line in the same direction, whose overall magnitude is found by adding their individual magnitudes together.

Vectors in Opposite Directions

Vectors acting in opposite directions, whose resultant magnitude is found by subtracting the smaller magnitude from the larger and acts in the direction of the larger vector.

Checking Vector Answers

A verification step ensuring vector answers include correct unit and direction, where resultant vectors for perpendicular components must be longer than either component but shorter than their arithmetic sum.