General Physics 1: Vectors and Vector Operations

Vocabulary flashcards covering key vector concepts from the lecture notes.

Vector quantity

A physical quantity that has both magnitude and direction.

Scalar quantity

A physical quantity described by magnitude only, with no direction.

Magnitude

The size or length of a vector (its numerical value).

Direction

The orientation that a vector points toward.

Displacement

A vector representing the change in position from start to end.

Velocity

A vector describing speed with direction; rate of change of position.

Speed

Rate of motion; magnitude of velocity.

Acceleration

Rate of change of velocity; a vector.

Force

Interaction that can cause a change in motion; a vector quantity.

Mass

Amount of matter; a scalar quantity.

Energy

Capacity to do work; a scalar quantity.

Volume

Amount of space occupied; a scalar quantity.

Weight

Gravitational force on a mass; a vector directed downward.

Momentum

Mass times velocity; a vector.

Impulse

Change in momentum; force applied over a time interval; a vector.

Area

Two-dimensional measure; a scalar quantity.

Density

Mass per unit volume; a scalar quantity.

Distance

Total length of travel; a scalar quantity.

Vector notation

How vectors are written, using arrows over letters or boldface.

Arrow representation

A vector drawn as an arrow; length represents magnitude and direction shows orientation.

Unit vector

A vector with magnitude 1 used to indicate direction.

i-hat, j-hat, k-hat

Unit vectors along the x, y, and z axes in 3D space.

Component form

Expressing a vector as V = Vx î + Vy ĵ (+ Vz k̂ in 3D).

Horizontal component

The x-component of a vector along the horizontal axis.

Vertical component

The y- (and z-) component of a vector along the vertical axis.

Resolution

Decomposing a vector into its horizontal and vertical components.

Resultant

The sum of two or more vectors.

Vector addition

Combining vectors to obtain a resultant.

Parallelogram method

Graphical method where the diagonal of the parallelogram represents the resultant.

Polygon method

Graphical method (tip-to-tail) for summing vectors by polygon completion.

Graphical method

Using pictures (parallelogram or polygon) to add vectors.

Analytical method

Using algebra and trigonometry (components, laws) to add vectors.

Law of Sines

sin(A)/a = sin(B)/b = sin(C)/c; used in triangles to relate angles and sides.

Law of Cosines

a² = b² + c² − 2bc cos(A); relates sides and angles of a triangle.

Dot product

A·B = AB cos θ; a scalar quantity representing the projection of one vector onto another.

Cross product

A×B = AB sin θ; a vector perpendicular to both A and B.

Angle between vectors

The smallest angle θ between two vectors, used in dot/cross products.

Negative vector

The vector with the same magnitude but opposite direction, written as −V.

Subtraction

A − B = A + (−B); vector difference.

Scalar multiplication

Multiplying a vector V by a scalar k to yield kV, scaling magnitude.

Tailwind

Wind velocity in the same direction as the motion; affects ground velocity.

Headwind

Wind velocity opposite to the motion; reduces ground velocity.

Ground velocity

Velocity of an object relative to the ground; sum of air velocity and wind.

Air velocity

Velocity of an object through the surrounding air.

3D vectors

Vectors in space with x-, y-, and z- components.

Unit vectors in space

î, ĵ, k̂ form the basis in 3D space; V = Vx î + Vy ĵ + Vz k̂.

3D magnitude

Magnitude of a 3D vector: sqrt(Vx² + Vy² + Vz²).

Displacement vs distance

Displacement is a vector (change in position); distance is the scalar length traveled.

Direction notations (N of E, etc.)

Descriptive ways to express a vector’s direction, e.g., 30° North of East.

Cardinal directions

N, E, S, W—the primary compass directions.

Intermediate directions

NE, NW, SE, SW—directions halfway between cardinal points.

Vector resolution in 3D

Decomposing a 3D vector into its x, y, z components.

Work

W = F · d; the work done by a force along a displacement (scalar product).

Torque

τ = r × F; the rotational effect (moment) of a force.

F = ma

Newton’s second law: net force equals mass times acceleration.