Principle Library

Deep dives into specific concepts. Each principle guide covers derivations, applications, and common pitfalls.

60 principles across 1 domains

Physics

Classical Mechanics (60)

Acceleration - Derivative Definition: Instantaneous Rate of Change

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Angular Acceleration - Derivative Definition: Instantaneous Rotational Change

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Angular Displacement Integral Relation

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Angular Impulse Formula: When Torque Over Time Changes Angular Momentum

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Angular Impulse-Angular Momentum Theorem (Integral): Time-Varying Torque

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Angular Momentum (Particle): Rotational Motion About a Point

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Angular Momentum (Rigid Body): Master Rotational Dynamics

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Angular Velocity - Derivative Definition: How Rotation Rate Changes

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Angular Velocity Change: Integral Form for Rotational Kinematics

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Arc Length-Angle Relation: Connecting Linear and Rotational Motion

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Center of Mass (Position): Locating the Balance Point

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Center of Mass (Velocity): Finding the Average Motion

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Centripetal Acceleration: Understanding Acceleration in Circular Motion

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Conservation of Angular Momentum

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Conservation of Linear Momentum

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Displacement-Integral Relation: Finding Position from Velocity

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Gravitational Potential (Near Surface): Mastering the mgh Formula

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Hooke's Law: Understanding Spring Force and Elastic Behavior

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Impulse-Momentum Theorem (Algebraic): Impulse Equals Momentum Change

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Impulse-Momentum Theorem (Integral): General Time-Varying Forces

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Kinematics 1 - Algebraic: Predicting Position Under Constant Acceleration

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Kinematics 2 - Algebraic: Velocity as a Function of Time

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Kinematics 3: Velocity-Position Relation

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Kinematics 4: Displacement from Average Velocity

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Kinetic Friction: Understanding Sliding Resistance in Mechanics

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Linear Momentum (Definition): Quantifying Motion's Persistence

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Mechanical Energy Conservation: Master Energy Transformations

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Mechanical Energy with Non-Conservative Work: Tracking Energy Transfers

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Moment of Inertia - Integral Definition: Continuous Mass Distributions

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Moment of Inertia (Discrete): Quantifying Rotational Inertia

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Newton's First Law (Rotation): Rotational Equilibrium

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Newton's First Law (Translation): When Forces Balance

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Newton's Law of Gravitation: Understanding Universal Attraction

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Newton's Second Law - Momentum Form: Force as Rate of Change

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Newton's Second Law (Rotation): Connecting Torque to Angular Acceleration

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Newton's Second Law (Translation): The Foundation of Force and Motion

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Newton's Third Law: Identify Action–Reaction Pairs

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Parallel Axis Theorem: Shifting Rotational Inertia

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Power - Derivative Form: Instantaneous Rate of Energy Transfer

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Power (Algebraic): Calculating Energy Transfer Rate

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Power (Rotation): Instantaneous Rate of Rotational Energy Transfer

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Rotational Kinematics 1: Angular Position Under Constant Angular Acceleration

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Rotational Kinematics 2: Angular Velocity with Constant Angular Acceleration

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Rotational Kinematics 3: Angular Velocity Without Time

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Rotational Kinematics 4: Angular Displacement via Average Angular Velocity

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Rotational Kinetic Energy: Master Energy in Rotating Systems

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Rotational Work: Energy from Constant Net Torque

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Spring Potential Energy: Elastic Energy Storage

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Static Friction: Understanding the Force that Prevents Sliding

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Tangential Acceleration: Connecting Linear and Rotational Motion

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Tangential Speed: Connecting Linear and Angular Motion

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Torque - Angular Momentum Form: Rotational Dynamics in Calculus Form

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Torque (Definition): Measuring Rotational Force Effectiveness

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Translational Kinetic Energy: Understanding Motion's Energy

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Translational Work: Energy from Constant Force

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Velocity - Derivative Definition: Instantaneous Rate of Position Change

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Velocity Change - Integral Relation: Find Velocity from Acceleration

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Weight (Near Surface): Understanding Gravitational Force in Local Contexts

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Work - Integral Definition: Computing Work Along Arbitrary Paths

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Work-Energy Theorem: Connect Force to Speed

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