Torque Course

Lesson 1 • The Torque Equation Explained

Derives the core equation τ = r × F and explains each variable's role. Students apply the equation to simple lever and wrench scenarios.

Lesson 2 • Direction and Sign Conventions

Establishes clockwise vs. counterclockwise sign conventions and the right-hand rule. Correct sign usage prevents calculation errors in multi-force problems.

Lesson 3 • Key Physical Quantities in Rotation

Introduces angular displacement, velocity, and acceleration as rotational analogs to linear motion. Connects these quantities to torque production and measurement.

Lesson 4 • Visualizing Torque with Free-Body Diagrams

Teaches construction of free-body diagrams that include rotational forces. Diagrams serve as the primary problem-solving tool throughout the course.

Lesson 1 • Torque in Two and Three Dimensions

Extends torque analysis beyond planar problems to 3D vector cross products. Prepares students for complex machinery and multi-axis loading scenarios.

Lesson 2 • Resolving Forces into Components

Applies trigonometry to decompose forces into perpendicular and parallel components. Only the perpendicular component contributes to torque about a pivot.

Lesson 3 • Multiple Forces and Net Torque

Calculates net torque when several forces act on a single body. Introduces algebraic summation of torques with consistent sign conventions.

Lesson 4 • Understanding the Moment Arm

Defines the moment arm as the perpendicular distance from the pivot to the line of action. Explains why this distance, not total length, governs torque.

Lesson 1 • Torque in Structural Connections

Analyzes torque at bolted joints, hinges, and pin connections in structures. Connects static analysis to real fastener and joint design decisions.

Lesson 2 • Solving Beam and Lever Problems

Applies equilibrium equations to beams with distributed and point loads. Develops systematic problem-solving habits for structural torque analysis.

Lesson 3 • Center of Gravity and Torque

Explains how an object's center of gravity acts as a single gravitational torque source. Locating the center of gravity is essential for stability analysis.

Lesson 4 • Conditions for Static Equilibrium

States both translational and rotational equilibrium conditions. Emphasizes that zero net torque is required alongside zero net force for full equilibrium.

Lesson 1 • Newton's Second Law for Rotation

Applies τ = Iα to predict angular acceleration from net torque. Links rotational dynamics directly to torque and inertia values.

Lesson 2 • Parallel Axis and Perpendicular Axis Theorems

Extends inertia calculations to off-center axes using the parallel axis theorem. The perpendicular axis theorem handles planar objects with multiple axes.

Lesson 3 • Moment of Inertia Fundamentals

Defines moment of inertia as rotational resistance dependent on mass distribution. Contrasts it with mass to clarify why geometry matters in rotation.

Lesson 4 • Calculating Inertia for Common Shapes

Provides formulas for disks, rods, rings, and rectangular plates. Students select and apply the correct formula for standard mechanical components.

Lesson 1 • Torque Impulse and Angular Impulse

Defines angular impulse as the product of torque and time, equal to the change in angular momentum. Solves problems involving brief torque applications.

Lesson 2 • Angular Momentum in Multi-Body Systems

Extends angular momentum analysis to systems with multiple interacting rotating bodies. Covers internal torques, gear trains, and coupled rotors.

Lesson 3 • Gyroscopic Effects and Precession

Explains how a spinning body resists changes in orientation and precesses under applied torque. Relevant to gyroscopes, flywheels, and rotating machinery.

Lesson 4 • Conservation of Angular Momentum

States that angular momentum is conserved when net external torque is zero. Applies conservation to spinning bodies, collisions, and figure-skater scenarios.

Lesson 1 • Torque, Speed, and Power Relationships

Derives P = τω and connects power, torque, and rotational speed. Students calculate any variable given the other two for motors and driven loads.

Lesson 2 • Shaft Torsion and Stress Analysis

Applies torsion theory to calculate shear stress and angular twist in circular shafts. Ensures shafts are sized to carry required torque without failure.

Lesson 3 • Belt and Chain Drive Torque Transfer

Calculates torque transmitted by belt and chain drives using tension differences. Addresses slip, pre-tension, and maximum load capacity.

Lesson 4 • Gear Systems and Torque Multiplication

Analyzes how gear ratios amplify or reduce torque and speed between shafts. Covers spur, helical, and bevel gear torque calculations.

Lesson 1 • Common Tightening Errors and Prevention

Identifies over-torquing, under-torquing, galling, and embedment relaxation as key failure modes. Prevention strategies reduce rework and joint failures in service.

Lesson 2 • Fastener Preload and Clamp Force

Connects applied torque to bolt preload and resulting clamp force using the torque-tension relationship. Friction coefficients and lubrication significantly affect this relationship.

Lesson 3 • Torque Specifications and Standards

Interprets manufacturer and industry torque specifications for fasteners and assemblies. Covers torque tables, grade markings, and specification hierarchies.

Lesson 4 • Tightening Strategies and Techniques

Compares torque-only, torque-plus-angle, and yield-controlled tightening methods. Each method offers different accuracy and joint integrity trade-offs.

Lesson 1 • Torque Optimization in System Design

Applies optimization techniques to minimize required torque while meeting performance targets. Covers gear ratio selection, mass reduction, and layout optimization.

Lesson 2 • Dynamic Torque Loads and Fatigue

Analyzes fluctuating and impact torque loads that cause fatigue in rotating components. Applies fatigue life concepts to shafts, gears, and fasteners.

Lesson 3 • Torsional Vibration and Resonance

Models torsional natural frequencies and identifies resonance conditions in drive trains. Damping and detuning strategies prevent destructive vibration.

Lesson 4 • Design Validation and Testing

Establishes methods for validating torque-related designs through analysis, simulation, and physical testing. Covers acceptance criteria and documentation practices.