AP Physics 1 Comprehensive Notes - Unit 1: Kinematics

AP Physics 1 Comprehensive Notes

Unit 1: Kinematics

Introductory Concepts:

Vector: Magnitude and Direction
- Magnitude means the "amount" of the vector or the value of the vector without direction.
Scalar: Magnitude only, no direction.
Component Vectors:
- Theta ( $\theta$ ) won’t always be with the horizontal, so the component in the x-direction won’t always use cosine.
- $\sin\theta = \frac{O}{H} = \frac{A_x}{A} \Rightarrow A_x = A\sin\theta$

Kinematics:

Distance vs. Displacement

Distance is how far something moves and includes the path traveled.
- Distance is a scalar.
Displacement is the straight-line distance from where the object started to where it ended.
- Displacement is a vector.
- Displacement is the change in position of an object: $\Delta x = x_f - x_i$

Speed and Velocity

Speed: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ (scalar quantity).
Velocity: $\bar{v} = \frac{\Delta x}{\Delta t}$ (vector quantity).

Acceleration

$\bar{a} = \frac{\Delta v}{\Delta t}$ (vector quantity).
The slope of a position vs. time graph is velocity.
The slope of a velocity vs. time graph is acceleration.
On an acceleration vs. time graph, the area under the curve represents the change in velocity.
On a velocity vs. time graph, the area under the curve represents displacement.

Free Fall

Acceleration due to gravity: $a_y = -g = -9.81 \frac{m}{s^2}$
An object is in free fall if the only force acting on it is gravity.

Uniformly Accelerated Motion (UAM) Equations:

AP Physics 1 Equation Sheet	Flipping Physics®
$v_x = v_{x0} + a_x t$	$v_f = v_i + a \Delta t$
$x = x_0 + v_{x0} t + \frac{1}{2} a_x t^2$	$\Delta x = v_i \Delta t + \frac{1}{2} a \Delta t^2$
$v_x^2 = v_{x0}^2 + 2 a_x (x - x_0)$	$v_f^2 = v_i^2 + 2 a \Delta x$
$\Delta x = \frac{1}{2} (v_i + v_f) \Delta t$

Projectile Motion

x direction	y direction
$a_x = 0$ (constant velocity)	Free-Fall
$v_x = \frac{\Delta x}{\Delta t}$	$a_y = -g = -9.81 \frac{m}{s^2}$

$\Delta t$ is the same in both directions because it is a scalar and has magnitude only (no direction).

Break initial velocity into components using SOH CAH TOA.
Use Pythagorean theorem to determine resultant vector magnitude.

Relative Motion

Vector Addition is used for relative motion.
Draw vector diagrams and break vectors into components.

Center of Mass

For non-rotational motion, the center of mass moves like a single particle.
In projectile motion, analyzing the center of mass simplifies calculations.