AP PHYSICS 1

UNIT 1: KINEMATICS

Motion - Defined as the change in position of an object over time.
Frame of Reference - A system for specifying the precise location of objects in space-time.

Observations

• Observing the motion of trains from a platform versus from another train illustrates the importance of the frame of reference.
  

Scalars and Vectors

• Scalar: A quantity that has only magnitude (e.g., distance, speed).

• Vector: A quantity that has both magnitude and direction (e.g., displacement, velocity).
  

Displacement

• Displacement (9;dX') is the vector quantity that refers to the change in position of an object. It can be calculated as:
    $ext{Displacement (dX)} = ext{Final Position} - ext{Initial Position}$
    - Example: Moving from 2 meters east to 5 meters east results in a displacement of 3 meters east.
  

Speed and Velocity

• Speed: A scalar quantity that measures how fast an object moves. It is calculated as:
    $ext{Speed} = rac{ ext{Distance}}{ ext{Time}}$

• Velocity: A vector quantity that includes both speed and direction.
  

Acceleration

• Defined as the rate of change of velocity over time.

• Positive acceleration occurs when an object speeds up, while negative acceleration (deceleration) occurs when it slows down.
  

Position vs. Time Graphs

• A position-time graph illustrates how an object's position changes over time. The slope of the graph represents speed or velocity.

• A steeper slope indicates a greater speed, while a negative slope indicates motion in the opposite direction.

Velocity and Acceleration Graphs

• The slope of a velocity-time graph indicates acceleration, while the area under the curve between the graph and the x-axis shows displacement.
  

Equations of Motion

Basic Kinematic Equations

1. $v = v_0 + at$
      - where:
        - $v$ = final velocity
        - $v_0$ = initial velocity
        - $a$ = acceleration
        - $t$ = time

2. $x = v_0t + rac{1}{2}at^2$
      - where:
        - $x$ = displacement

3. $v^2 = v_0^2 + 2ax$
      - relates final velocity to displacement and acceleration.
   

Examples of Kinematic Calculations

1. A jogger moves 4 meters north and then 3 meters south. The total displacement can be calculated:
      - $ext{Displacement} = 4m - 3m = 1m ext{ North}$

2. If a car travels 100 meters east in 5 seconds, the average velocity is:
      - $ext{Average Velocity} = rac{100m}{5s} = 20 ext{ m/s east}$

3. A car starting from rest accelerates at 2 m/s² for 3 seconds:
      - Initial velocity $v_0 = 0$
      - $a = 2 ext{ m/s}^2$, $t = 3 ext{ s}$
      - Displacement:
      $x = v_0t + rac{1}{2}at^2 = 0 + rac{1}{2}(2)(3^2) = 9 m$
   

Distance vs. Displacement

• Distance refers to the total ground covered by an object.

• Displacement measures the change in position and can be positive or negative.
  

Motion Maps and Dot Diagrams

• Motion maps or dot diagrams visually represent the position of an object with dots spaced according to distance traveled and time.
     - Dots closer together imply the object is slowing down.
     - Dots further apart indicate the object is speeding up.

UNIT 2: FORCE AND TRANSLATIONAL DYNAMICS

Force

• Defined as a push or pull applied to an object; characterized as a vector.
  

Types of Forces

1. Contact Forces: Forces that occur when two objects are in contact.
      - Examples:
        - Tension Force (T): The force exerted along the length of a string or rope.
        - Normal Force (N): The upward force exerted by a surface to support an object resting on it.
        - Friction Force (f): Occurs when two surfaces slide against each other.

2. Non-Contact Forces: Forces that act at a distance.
      - Examples:
        - Gravitational Force (F_g): The force that attracts objects toward the Earth.
        - Electromagnetic Forces: Forces acting between charged particles.
   

Free-Body Diagram

• A graphical representation of all the forces acting on an object, showing the direction and magnitude of each force.
  

Newton's Laws of Motion

1. First Law: An object at rest stays at rest, and a moving object continues to move at constant velocity unless acted upon by a net external force.
      - Example: An object resting on the ground remains there unless a net force acts upon it.

2. Second Law: The acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.
      - Formula:
      $F_{net} = ma$
      - Where $F_{net}$ is the net force, $m$ is mass, and $a$ is acceleration.

3. Third Law - For every action, there is an equal and opposite reaction.
      - Example: If you push against a wall, the wall pushes back with equal force.
   

Friction Force

• Acts between two surfaces in contact.
     - Static Friction (f_s): The initial force required to overcome the inertia of an object at rest.
     - Kinetic Friction (f_k): The force resisting motion between two surfaces in motion.
     - Depends on the nature of the surfaces and the normal force acting on these surfaces.
  

Tension Force

• The force transmitted through a string, rope, or cable when it is pulled tight by forces acting at each end.
     - Always acts along the length of the string.
  

System Overview

1. Analyzing any interactions between objects using the free-body diagram.

2. The use of friction affects the movement of objects and is always opposite to the direction of motion.

UNIT 3: WORK, ENERGY, AND POWER

Work

• Work is done when a force causes displacement in an object.

• Formula:
  $W = F imes d imes ext{cos}( heta)$
  

Energy

• Defined as the capacity of an object to do work:

1. Kinetic Energy (KE): Energy of an object in motion.
      - Formula:
      $KE = rac{1}{2} mv^2$

2. Potential Energy (PE): Stored energy based on position.
      - For gravitational potential energy:
      $PE = mgh$
      - Where $h$ is the height above a reference point.
   

The Work-Energy Theorem

• States that the net work done by the forces acting on an object is equal to the change in kinetic energy of the object.
     - $W_{net} = riangle KE$

• Conservation of energy states that energy cannot be created or destroyed, only transformed.
  

Power

• The rate at which work is done.
     - Formula:
     $P = rac{W}{t}$
  

Principles of Conservation

• In mechanical systems, energy is conserved unless acted upon by non-conservative forces like friction.

UNIT 4: LINEAR MOMENTUM

Momentum

• Defined as the product of an object's mass and its velocity.
     - Formula:
     $p = mv$
     - where $p$ is momentum, $m$ is mass, and $v$ is velocity.
  

Conservation of Momentum

• In an isolated system with no net external forces, the total momentum remains constant.
     $p_{initial} = p_{final}$
  

Impulse

• Defined as the change in momentum resulting from a net force applied over time:
     - $ext{Impulse} = F imes riangle t = riangle p$
     - Where $riangle p$ represents the change in momentum.

Types of Collisions

1. Elastic Collision: Both momentum and kinetic energy are conserved.

2. Inelastic Collision: Momentum is conserved, but kinetic energy is not conserved; some energy is lost in the form of heat or sound.
      - Perfectly Inelastic Collision: Maximum loss of kinetic energy; both objects stick together post-collision.
   

Coefficient of Restitution

• Used to measure the elasticity of a collision. -Values range between 0 (perfectly inelastic) and 1 (perfectly elastic).

UNIT 5: TORQUE AND ROTATIONAL DYNAMICS

Rotational Motion

• Described similarly to linear motion with angular quantities.
    - Angular Position ($ heta$), Angular Velocity ($ ext{ω}$), Angular Acceleration ($ ext{α}$).

Torque

• Defined as the rotational analog of force. It measures the effectiveness of a force to produce rotational motion.
     - Formula:
     $au = r imes F imes ext{sin}( heta)$
     - Where $au$ is torque, $r$ is the distance from the pivot point to the point of application of the force, and $heta$ is the angle between the force vector and the lever arm.

Moment of Inertia

• Defined as the measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution relative to the axis of rotation. - Formula: (I = rac{1}{2} m r^2) for solid cylinders.

Newton's Laws in Rotational Form

1. First Law: An object in rotational motion will remain in that state unless acted upon by a net external torque.

2. Second Law: The net torque acting on an object equals the moment of inertia multiplied by angular acceleration:
      - $au_{net} = I imes ext{α}$

Angular Momentum

• Defined as the product of an object's moment of inertia and its angular velocity.
     - Formula: (L = I ext{ω})

• Angular momentum is conserved in closed systems where no external torques are acting.

UNIT 6: ENERGY AND MOMENTUM OF ROTATING SYSTEMS

Rotational Kinetic Energy

• Defined for objects rotating with a specified angular velocity:
     - Formula:
     $KE_{rotational} = rac{1}{2} I ext{ω}^2$

Conservation of Energy in Rotational Systems

• Total Mechanical Energy (TME) is constant in closed systems unless acted on by non-conservative forces.
     

Angular Impulse

• Defined as the product of the net torque and the time duration:
     $ext{Angular Impulse} = au imes riangle t$

UNIT 7: OSCILLATIONS

Simple Harmonic Motion (SHM)

• A type of periodic motion where an object moves back and forth around an equilibrium position.
     - Example: Mass on a spring or a pendulum.

Energy in SHM

• Total energy is conserved and the sum of kinetic and potential energy.
     - $E_{total} = KE + PE$
     - The potential energy can be stored in springs or gravitational fields.

UNIT 8: FLUIDS

Properties of Fluids

• Density: Defined as mass per unit volume.
     - $<br>ho = rac{m}{V}$

• Pressure: The ratio of force over area; important in fluid statics.
     - Formula:
     $P = rac{F}{A}$

• Archimedes' Principle: States that the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object.

Fluid Dynamics

• Continuity Equation: Describes the conservation of mass in fluid flow.
     - $A_1V_1 = A_2V_2$

• Bernoulli’s Principle: States that in a streamline flow, an increase in fluid velocity occurs simultaneously with a decrease in pressure.