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#AP Physics 1: Ultimate Study Guide 🚀

Hey, future physicist! Let's get you prepped for the AP Physics 1 exam. Remember, you've got this! 💪

#Table of Contents

Unit 1: Kinematics
Unit 2: Dynamics
Unit 3: Circular Motion and Gravitation
Unit 4: Energy
Unit 5: Momentum
Unit 6: Simple Harmonic Motion
Unit 7: Torque and Rotational Motion
Final Exam Focus
Practice Questions

# Unit 1: Kinematics 🚗

#1.1 Motion in One Dimension

Displacement, Velocity, and Acceleration:
- Displacement (Δx) is the change in position. It's a vector!
- Velocity (v) is the rate of change of displacement. Also a vector!
- Acceleration (a) is the rate of change of velocity. Yep, it's a vector too!
Key Equations:
- $v = \frac{\Delta x}{\Delta t}$ (average velocity)
- $a = \frac{\Delta v}{\Delta t}$ (average acceleration)
- Kinematic Equations (for constant acceleration):
  - $v_f = v_i + at$
  - $\Delta x = v_i t + \frac{1}{2}at^2$
  - $v_f^2 = v_i^2 + 2a\Delta x$
  - $\Delta x = \frac{1}{2}(v_i + v_f)t$

Key Concept

Remember to use the correct sign conventions for direction (e.g., right/up is positive, left/down is negative).

Graphs of Motion:
- Position vs. Time: Slope = velocity
- Velocity vs. Time: Slope = acceleration, Area = displacement
- Acceleration vs. Time: Area = change in velocity

#1.2 Motion in Two Dimensions

Projectile Motion:
- Analyze horizontal and vertical motion separately.
- Horizontal motion: constant velocity ( $a_x = 0$ )
- Vertical motion: constant acceleration due to gravity ( $a_y = -g = -9.8 m/s^2$ )
- Initial velocity components: $v_{ix} = v_i \cos(\theta)$ , $v_{iy} = v_i \sin(\theta)$

Exam Tip

Remember that time is the same for both horizontal and vertical motion.

Relative Motion:
- Velocity of an object relative to a frame of reference.
- Use vector addition to find relative velocities.

Memory Aid

Think of projectile motion as a combination of a horizontal car moving at constant speed and a ball being thrown straight up and down. They happen at the same time, but are independent of each other.

Practice Question

Multiple Choice:

A ball is thrown horizontally from the top of a building. If air resistance is negligible, what is the shape of the ball's trajectory? (A) A straight line (B) A parabola (C) A circle (D) A hyperbola
A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the average acceleration of the car? (A) 2 m/s² (B) 4 m/s² (C) 5 m/s² (D) 10 m/s²

Free Response: A projectile is launched with an initial velocity of 30 m/s at an angle of 60 degrees above the horizontal. Neglect air resistance.

(a) Calculate the horizontal and vertical components of the initial velocity. (2 points) (b) Calculate the time it takes for the projectile to reach its maximum height. (2 points) (c) Calculate the maximum height reached by the projectile. (2 points) (d) Calculate the total time the projectile is in the air. (2 points) (e) Calculate the horizontal range of the projectile. (2 points)

Answer Key:

*Multiple Choice: 1. (B), 2. (B)

Free Response:

(a) $v_{ix} = 30 \cos(60) = 15 m/s$ , $v_{iy} = 30 \sin(60) = 26 m/s$ (2 points) (b) $v_f = v_i + at$ , $0 = 26 - 9.8t$ , $t = 2.65 s$ (2 points) (c) $\Delta y = v_i t + \frac{1}{2}at^2$ , $\Delta y = 26(2.65) - 4.9(2.65)^2 = 34.4 m$ (2 points) (d) Total time = 2 * time to max height = 2 * 2.65 = 5.3 s (2 points) (e) $x = v_x t = 15 * 5.3 = 79.5 m$ (2 points)

# Unit 2: Dynamics 🏋️‍♀️

#2.1 Forces and Newton's Laws

Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net force.
Newton's Second Law: $F_{net} = ma$ . The net force on an object is equal to its mass times its acceleration.
Newton's Third Law: For every action, there is an equal and opposite reaction.

Newton's Second Law is the foundation of dynamics. Make sure you understand how to apply it in various scenarios.
Types of Forces:
- Gravity: $F_g = mg$ (weight)
- Normal Force: Force exerted by a surface perpendicular to the surface.
- Tension: Force exerted by a string or rope.
- Friction: Force that opposes motion. $F_f = \mu F_N$ (static or kinetic)

Common Mistake

Don't forget to draw free-body diagrams to visualize all forces acting on an object.

#2.2 Applications of Newton's Laws

Inclined Planes:
- Resolve forces into components parallel and perpendicular to the plane.
- $F_{g\parallel} = mg \sin(\the...

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Ohm’s Law, Kirchhoff’s Loop Rule (Resistors in Series and Parallel)

Joseph Brown