Vectors and Two-Dimensional Kinematics (Ch 3 & 4)

Vocabulary flashcards covering scalars vs vectors, vector components, vector addition, projectile motion, and relative velocity from Chapters 3 and 4.

Scalar

A quantity described by magnitude only (no direction) and has units.

Vector

A quantity described by both magnitude and direction.

Magnitude

The size or length of a vector, computed from its components.

Direction

The orientation of a vector in space, independent of its magnitude.

Displacement

A vector representing the straight-line change in position; has components Δx and Δy.

Vector components

The x- and y-components of a vector obtained by resolving it along perpendicular axes.

x-component (vx)

The component of a vector along the x-axis.

y-component (vy)

The component of a vector along the y-axis.

Vector magnitude formula

If components are vx and vy, the magnitude is v = sqrt(vx^2 + vy^2).

Direction angle

The angle θ of a vector with respect to the x-axis, given by tan(θ) = vy/vx.

Pythagorean theorem (vectors)

Used to combine perpendicular components to find the resultant magnitude.

Triangle (geometric) method

Head-to-tail method of adding vectors to obtain the resultant.

Analytical Component Method

Break vectors into components, add like components (x with x, y with y), then recombine to get magnitude and direction.

Negative of a vector

A vector with the same magnitude but opposite direction; adding a negative equals subtraction.

Unit vectors

Fixed-direction vectors (e.g., i for x, j for y) used to express other vectors.

Vector addition

The process of combining two vectors to produce a resultant vector.

Projectile Motion

Motion of a body under gravity only (often neglecting air resistance); acceleration is downward.

Horizontal and vertical components in projectile motion

Analyze x and y motions separately since ax = 0 and ay = -g (constant downward acceleration).

Range (projectile)

Maximum horizontal distance traveled by a projectile in the absence of air resistance.

Maximum height (projectile)

Highest vertical position reached; H = (v0^2 sin^2 θ)/(2g) for launch with initial speed v0 at angle θ (no air resistance).

Launch angle for maximum range (no air resistance)

45 degrees yields the maximum range when air resistance is neglected.

Relative Velocity

Velocity of an object as measured in a particular inertial reference frame; depends on the frame.

Velocity in a new frame (v_rel)

The velocity of an object relative to another frame, often computed as vobject − vframe.

Two-dimensional relative velocity

In 2D, velocity components and the observed angle can change with the reference frame.

Common time in 2D kinematics

When solving 2D problems, the x- and y-components share the same time variable.

Acceleration not parallel to velocity

If acceleration and velocity are not parallel, the path is curved and direction changes over time.