Vector Physics and Relative Velocity

Flashcards covering vector operations, force and velocity components, vector properties, and relative velocity calculations based on lecture notes.

Resultant Vector

The single vector that represents the combined effect or sum of two or more vectors acting together, such as $V_{res} = v_A + v_B$.

Same-Direction Forces Rule

The magnitude of the resultant force when two forces act in the same direction, calculated using algebraic addition: $f = f_1 + f_2$.

Opposite-Direction Forces Rule

The magnitude of the resultant force when two forces act in opposite directions, calculated using subtraction: $f = f_1 - f_2$.

Perpendicular Forces Rule

The magnitude of the resultant force when two forces act perpendicular to each other, calculated using the Pythagorean theorem: $f = \backslash sqrt{f_1^2 + f_2^2}$.

Arrow Length in Vector Scale

The visual representation of a vector's magnitude in graphical scale drawings (e.g., $1\backslash ,cm = 1\backslash ,m/s$).

Vector Translation Property

The rule stating that any vector can be moved or translated to a new position as long as its magnitude (arrow length) and direction remain unchanged.

Negative Sign in Vectors

A sign indicating that a vector acts in the exact opposite direction to the designated positive direction (e.g., if East is positive, West is negative).

Horizontal Force Component ($F_x$)

The horizontal projection of a force vector, given by $F_x = F \backslash cos(\backslash alpha)$.

Vertical Force Component ($F_y$)

The vertical projection of a force vector, given by $F_y = F \backslash sin(\backslash alpha)$.

Horizontal Velocity Component ($v_x$)

The horizontal projection or component of a velocity vector, given by $v_x = v \backslash cos(\backslash alpha)$.

Vertical Velocity Component ($v_y$)

The vertical projection or component of a velocity vector, given by $v_y = v \backslash sin(\backslash alpha)$.

Relative Velocity ($v_{AB}$)

The velocity of object B with respect to object A, calculated as $v_{AB} = v_B - v_A$.

Symmetric Relative Velocity Property

The relationship showing that the velocity of object A relative to B is equal in magnitude and opposite in sign to the velocity of B relative to A: $v_{BA} = -v_{AB}$.

Vector Direction Angle ($ackslash theta$)

The angle a vector makes relative to an axis, determined by the trigonometric relation $\backslash tan(\backslash theta) = \backslash frac{y}{x}$.