2-D Kinematics and Vectors Flashcards

Vocabulary and key concepts from Introduction to Newtonian Mechanics covering 2-D Kinematics, Vectors, Relative Motion, and Circular Motion.

$$\hat{i}$$

The unit vector in the $+x$ direction.

$$\hat{j}$$

The unit vector in the $+y$ direction.

$A_x$ (Vector Component)

The x-component of a vector, calculated as $A ext{cos}( heta)$.

$A_y$ (Vector Component)

The y-component of a vector, calculated as $A ext{sin}( heta)$.

Vector addition by components

A process where components are added individually such that if $\vec{C} = \vec{A} + \vec{B}$, then $\vec{C} = (A_x + B_x)\hat{i} + (A_y + B_y)\hat{j}$.

2D motion analysis

The method of breaking motion into two directions (horizontal and vertical) and analyzing them separately.

Horizontal Motion (Projectile)

Motion characterized by constant velocity where acceleration $a_x = 0$.

Vertical Motion (Projectile)

Motion characterized by constant acceleration where $a_y = -g$.

Range $R$

The horizontal distance traveled by a projectile on level ground for which air resistance is negligible.

$$\vec{v}<em>{a \rightarrow c} = \vec{v}</em>{a \rightarrow b} + \vec{v}_{b \rightarrow c}$$

The formula for relative motion where 'a' is the object, 'b' is a moving frame (e.g., a train), and 'c' is a stationary frame (e.g., the ground).

Angular velocity ($\omega$)

The rate at which the angle $\theta$ changes, measured in $\text{rad/s}$, defined as $\omega = \frac{d\theta}{dt} = \frac{2 ext{\pi}}{T}$.

Uniform Circular Motion

Motion where acceleration occurs due to the change in the direction of velocity, even if speed is constant.

Centripetal Acceleration ($a_c$)

Acceleration toward the center of a circular path, expressed as $a_c = \frac{v^2}{R}$ or $a_c = \omega^2R$.