Course Clarity Map

Before MAE 202Prior-knowledge refreshers6 concepts

Module 1Kinematics of Particles — Describe Motion7 concepts

Module 2Kinetics of Particles — Explain Motion6 concepts

Module 3Kinematics of Rigid Bodies — Describe Connected Motion6 concepts

Module 4Kinetics of Rigid Bodies — Explain Connected Motion5 concepts

Module 5Work and Energy — Choose a More Efficient Method5 concepts

Final outcomeEngineering judgment1 concept

Change over timeFunctions and Calculus

Motion is described by quantities that change, so derivatives, integrals, and differential equations describe that change.

Relationships in spaceGeometry and Trigonometry

Once a physical situation is drawn, geometry and trigonometry turn the picture into measurable relationships.

Magnitude and directionVectors and Coordinate Components

Since motion and forces have direction, vectors separate a physical problem into solvable components.

Isolate the systemStatics and Free-Body Diagrams

Before studying changing motion, isolate objects and account for every force and moment acting on them.

Physical rulesIntroductory Mechanics and Energy

Newton's laws and energy methods provide the basic rules that this course extends to more complicated motion.

Numerical predictionMATLAB and Differential-Equation Tools

When motion equations cannot be solved cleanly by hand, numerical tools predict how systems evolve.

Start with measurementPosition, Velocity, and Acceleration

Turn motion into measurable quantities.

More than one directionCurvilinear Motion and Degrees of Freedom

Since particles do not always move along one line, identify the independent coordinates needed to describe their path.

Fixed x–y directionsCartesian and Projectile Motion

With motion separated into x- and y-components, predict motion through space.

Follow the pathNormal–Tangential Coordinates

When the path itself matters, describe speed change along the path and direction change toward the curve.

Match the geometryPolar and Mixed Coordinates

When motion revolves around a point or combines constraints, choose coordinates that match the geometry.

Connected particlesDependent Motion

When one particle's movement constrains another, connect their positions, velocities, and accelerations.

Moving observersRelative Motion

When the observer is also moving, compare motions using a translating reference frame.

Ask what caused itFrom Kinematics to Kinetics

Now that motion can be described, ask which forces create that motion.

Model forcesFree-Body Diagrams and Equations of Motion

Since forces cause acceleration, convert a physical force diagram into equations.

Contact in fixed axesCartesian Kinetics and Friction

Apply force equations in fixed directions while accounting for contact and friction.

Forces along a pathCurved-Path Kinetics

Connect forces to changes in speed and changes in direction along a curved path.

Forces around a pointPolar Kinetics and Pendulums

For motion around a point, express force and acceleration in radial and transverse directions.

Choose compatible toolsMixed Particle Systems and Momentum

Real systems combine coordinate descriptions, constraints, and momentum relationships, so select a compatible solution strategy.

Connected particlesFrom Particles to Rigid Bodies

A rigid body is many connected particles, so its motion combines translation and rotation.

Fixed reference frameAbsolute Motion Analysis

Begin by describing the velocity and acceleration of each point from a fixed reference frame.

Points move togetherRelative Velocity and General Plane Motion

Since points on a rigid body move together, relate their velocities using translation and rotation.

Extend the relationshipRelative Acceleration

Extend the velocity relationship to include tangential and centripetal acceleration effects.

A useful instantInstantaneous Center of Rotation

At one instant, complicated planar motion can be understood as rotation around a special point.

Bodies meetContact, Rolling, and Slipping

When bodies touch, contact conditions determine how their motions constrain each other.

Forces and momentsRigid-Body Equations of Motion

Now that rigid-body motion is describable, connect external forces and moments to translation and rotation.

Where mass is locatedMass Moment of Inertia

Since rotational response depends on where mass is located, measure resistance to angular acceleration.

Complete body motionCoupled Translation and Rotation

Combine forces, moments, and inertia to predict complete rigid-body motion.

Test the outcomeSlip, Tip, and Rolling Outcomes

Determine which contact behavior is physically possible before solving the resulting motion.

Interacting bodiesMechanisms and Connected Rigid Bodies

Real machines contain interacting bodies, so combine constraints and equations across the full mechanism.

Compare statesWhy Use Energy?

Force equations track motion instant by instant; energy methods compare important starting and ending states.

Transfer through motionWork Done by Forces and Moments

To use energy, calculate how forces and moments transfer energy through motion.

Energy of motionKinetic Energy of Particles and Rigid Bodies

Represent translational and rotational motion as stored kinetic energy.

Recoverable energyPotential Energy and Conservative Forces

Some forces store recoverable energy, allowing motion to be analyzed without following the entire path.

Choose the clearest modelWork–Energy Method and Method Selection

Combine work, kinetic energy, and potential energy, then decide whether force equations or energy provides the clearest solution.

What the course builds towardPredict and Explain Real Motion

Choose useful coordinates, select an appropriate mechanics method, calculate the result, and defend whether it makes physical sense.