College Physics I: Chapter 3: Scalars, Vectors, and Motion

Flashcards covering key definitions and concepts related to scalars, vectors, vector operations, and basic kinematic quantities from College Physics I, Dr. Sneh Modi's lecture.

Scalar

A physical quantity that only has a magnitude and no direction.

Vector

A physical quantity that has both a magnitude and a direction.

Negative Scalar

Scalars can be negative, such as temperature.

Negative Vector

Vectors can be negative, such as velocity.

Frame of Reference

A system or set of coordinates used to specify the position and orientation of objects, necessary for defining direction.

Coordinate System

A system used to define positions in space, commonly 1D (line) or 2D (plane).

Vector Components

The projection of a vector onto the main directions (axes) of a coordinate system.

Magnitude of a Vector

Calculated as r² = x² + y² for a vector with components x and y.

Angle of a Vector

The direction of a vector, typically given with respect to an axis (e.g., +Ve x-axis), calculated as tan θ = y/x.

Vector Addition (Graphical Method)

Placing the second vector's tail on the head of the first, and drawing a resultant vector from the tail of the first to the head of the second.

Vector Subtraction

Can be found by using components, e.g., for C = 2A - B, Cx = 2Ax - Bx and Cy = 2Ay - By.

Unit Vector

A vector that purely represents a direction, having a magnitude of 1.

Unit Vectors (x-hat, y-hat)

Standard unit vectors in the x and y directions, used to express a vector in component form (A = Ax x̂ + Ay ŷ).

Position Vector (r)

A vector representing the position of a point with respect to the origin.

Displacement (Δr)

The change in position, calculated as final position (rf) minus initial position (ri), pointing from ri to rf.

Average Velocity (v_avg)

The total displacement divided by the time interval (Δr / Δt), with direction in the same direction as Δr.

Instantaneous Velocity (v)

The limit of Δr/Δt as Δt approaches zero; in the direction of the tangent at that point in time.

Acceleration

A change in velocity, which can be caused by changing speed (gas pedal, brake) or direction (steering wheel).