CELE Engineering Mechanics — Dynamics: KinematicsConcept Map

Concept

Rectilinear Motion

Sub Concepts

• Constant Acceleration Equations
• Variable Acceleration Integration
• Velocity Definition (ds/dt)
• Acceleration Definition (dv/dt)
• Free Fall (g = 9.81 m/s²)

Relationship To Central

Core kinematic form; motion along a straight line with constant or variable acceleration

Concept

Projectile Motion

Sub Concepts

• Horizontal Motion (Constant Velocity)
• Vertical Motion (Constant Acceleration)
• Range Calculation
• Maximum Height
• Time of Flight
• Launch Angle Effects
• Independence of Motion Components

Relationship To Central

Two-dimensional kinematic application; combines horizontal and vertical rectilinear motions

Concept

Rotational (Angular) Kinematics

Sub Concepts

• Angular Displacement (θ, radians)
• Angular Velocity (ω, rad/s)
• Angular Acceleration (α, rad/s²)
• Constant Angular Acceleration
• Linear-Angular Relationships (v = rω, a_t = rα)
• Centripetal Acceleration (a_n = v²/r = rω²)
• Revolution-to-Radian Conversion

Relationship To Central

Kinematics applied to rotating bodies; uses angular analogs of rectilinear parameters

Concept

Fundamental Kinematic Parameters

Sub Concepts

• Position (s, meters)
• Velocity (v, m/s)
• Acceleration (a, m/s²)
• Time (t, seconds)
• Initial Conditions (v₀, s₀)

Relationship To Central

Building blocks of all kinematic descriptions

Concept

Mathematical Relationships

Sub Concepts

• Differentiation (v = ds/dt, a = dv/dt)
• Integration (v = ∫a dt, s = ∫v dt)
• Constant-a Kinematic Trio
• Elimination of Time Variable
• Trigonometric Applications (Projectile Motion)

Relationship To Central

Quantitative tools that define kinematic equations

Concept

Common Board-Exam Problem Types

Sub Concepts

• Vehicle Acceleration/Braking
• Free-Fall Height/Impact Speed
• Projectile Clearance (Obstacles)
• Rotating Equipment (Flywheels, Wheels)
• Multi-Stage Motion Sequences

Relationship To Central

Practical assessment contexts for kinematic analysis

To

Fundamental Kinematic Parameters

From

Rectilinear Motion

Strength

strong

Relationship

Position, velocity, and acceleration are core parameters that rectilinear motion describes through time-dependent functions.

To

Free Fall

From

Rectilinear Motion

Strength

strong

Relationship

Free fall is a special case of rectilinear motion where acceleration is constant at g = 9.81 m/s² downward.

To

Rectilinear Motion

From

Projectile Motion

Strength

strong

Relationship

Projectile motion decomposes into two independent rectilinear motions: constant horizontal velocity and constant vertical acceleration (g).

To

Trigonometric Applications

From

Projectile Motion

Strength

strong

Relationship

Launch angle θ determines initial velocity components (v₀cosθ horizontal, v₀sinθ vertical) and appears in range and height formulas via sin2θ and sin²θ.

To

Fundamental Kinematic Parameters

From

Rotational Kinematics

Strength

strong

Relationship

Angular analogs (θ, ω, α) mirror rectilinear (s, v, a), providing parallel kinematic descriptions for rotating bodies.

To

Linear-Angular Relationships

From

Rotational Kinematics

Strength

strong

Relationship

A point at radius r on a rotating body links angular and linear motion: v = rω, a_t = rα, a_n = rω².

To

Rectilinear Motion

From

Mathematical Relationships

Strength

strong

Relationship

Calculus (derivatives and integrals) establishes the definitions v = ds/dt, a = dv/dt and enables solution of variable-acceleration problems.

To

Rotational Kinematics

From

Mathematical Relationships

Strength

strong

Relationship

Same calculus relationships apply: ω = dθ/dt, α = dω/dt, enabling solution of variable angular acceleration.

To

Rectilinear Motion

From

Constant Acceleration Equations

Strength

strong

Relationship

The three kinematic equations (v = v₀ + at, s = v₀t + ½at², v² = v₀² + 2as) are the primary tools for constant-a problems.

To

Rotational Kinematics

From

Constant Angular Acceleration

Strength

strong

Relationship

Angular analogs of the three kinematic equations (ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ) solve constant α problems.

To

Projectile Motion

From

Independence of Motion Components

Strength

strong

Relationship

Horizontal and vertical motions in a projectile are independent, sharing only time t; this is fundamental to projectile analysis.

To

Range Calculation

From

Launch Angle Effects

Strength

strong

Relationship

The range formula R = v₀²sin2θ/g shows that range depends critically on angle; maximum at 45°.

To

Rectilinear Motion

From

Variable Acceleration Integration

Strength

moderate

Relationship

When acceleration is not constant, integration of a(t) or a(v) or a(s) replaces the three kinematic equations.

To

Rotational Kinematics

From

Revolution-to-Radian Conversion

Strength

strong

Relationship

Conversion 1 rev = 2π rad and ω (rad/s) = 2πN/60 from rpm is essential before applying angular equations.

To

Rotational Kinematics

From

Centripetal Acceleration

Strength

strong

Relationship

A point on a rotating body has centripetal (normal) acceleration a_n = v²/r = rω² directed toward the axis.

To

Rectilinear Motion

From

Common Board-Exam Problem Types

Strength

strong

Relationship

Vehicle braking, free-fall height, and impact speed calculations are standard rectilinear kinematics problems.

To

Projectile Motion

From

Common Board-Exam Problem Types

Strength

strong

Relationship

Projectile clearance (clearing obstacles, walls) and impact angle calculations are typical board-exam applications.

To

Rotational Kinematics

From

Common Board-Exam Problem Types

Strength

strong

Relationship

Flywheel acceleration, wheel braking, and rpm-to-rad/s conversions are routine rotating-equipment problems.

To

Rectilinear Motion

From

Sign Conventions

Strength

strong

Relationship

Consistent choice of positive direction (up, down, left, right) determines the sign of velocity and acceleration; critical for correctness.

To

Constant Acceleration Equations

From

Time Variable Elimination

Strength

moderate

Relationship

The equation v² = v₀² + 2as eliminates time, allowing direct solution when t is not given or not useful.