Visighta

Curriculum

Chapter 1 · Start Here

Mathematical Description of Motion

7 lessons
Motion, models, and idealization in mechanics
Position as a function of time
Reference frames and coordinate systems
Displacement, path length, and trajectory
Velocity as the derivative of position
Acceleration as the derivative of velocity
Interpreting motion through graphs, formulas, and data
Chapter 2

One-Dimensional Kinematics

6 lessons
Motion on a line and sign conventions
Constant acceleration and its exact solutions
Nonuniform acceleration and integral relationships
Motion with piecewise-defined acceleration
Turning points, extrema, and qualitative analysis of motion
Kinematics from experimental position and velocity data
Chapter 3

Vector Kinematics in Two and Three Dimensions

7 lessons
Position, velocity, and acceleration vectors
Component form and changing bases
Parametric descriptions of trajectories
Projectile motion as a vector-valued model
Relative motion and moving reference frames
Tangential and normal components of acceleration
Circular motion and curvature-based intuition
Chapter 4

Differential Equations of Motion

5 lessons
From acceleration laws to differential equations
Solving simple initial-value problems in mechanics
Constant, linear, and velocity-dependent acceleration models
Approximation, linearization, and local models of motion
Numerical time stepping and Euler-type methods
Chapter 5

Forces and Newtonian Kinetics

7 lessons
Interactions, force models, and free-body diagrams
Newton's laws as the foundation of kinetics
Inertial mass and the equation $\sum \vec{F} = m\vec{a}$
Weight, tension, normal force, drag, and friction
Coupled systems and constraint forces
Equilibrium as a zero-acceleration special case
Modeling assumptions and limits of common force laws
Chapter 6

Applications of Translational Dynamics

5 lessons
Motion on inclines and connected-particle systems
Frictional motion and threshold behavior
Resistive forces and terminal speed
Nonconstant net force and acceleration as a state-dependent quantity
Choosing coordinates to simplify equations of motion
Chapter 7

Work and Kinetic Energy

7 lessons
Work as a line integral perspective in simple settings
Constant and variable forces
The work-kinetic energy theorem
Conservative forces and potential energy
Energy diagrams and qualitative motion analysis
Power and rates of energy transfer
Comparing Newton's-law and energy-based solution methods
Chapter 8

Momentum, Impulse, and Conservation Laws

6 lessons
Linear momentum and impulse
Momentum change from force over time
Conservation of momentum for isolated systems
Elastic and inelastic collisions
Two-dimensional collision analysis
Center-of-mass motion and system-level reasoning
Chapter 9

Rotational Kinematics

6 lessons
Angular position, angular velocity, and angular acceleration
Rotational motion with constant angular acceleration
Angular quantities as derivatives and integrals
Arc length, tangential speed, and centripetal acceleration
Translational-rotational analogies in kinematics
Rolling kinematics and constraints without slipping
Chapter 10

Torque and Rotational Kinetics

7 lessons
Torque as the rotational effect of force
Cross-product structure and lever arm interpretation
Rotational equilibrium and balance
Moment of inertia from mass distribution
Newton's second law for rotation: $\sum \tau = I\alpha$
Coupled translation and rotation in rigid-body motion
Choosing axes and simplifying rotational dynamics problems
Chapter 11

Rotational Work, Energy, and Angular Momentum

6 lessons
Rotational kinetic energy
Work done by torques
Angular momentum of particles and rigid bodies
Angular impulse and angular momentum change
Conservation of angular momentum
Energy and angular momentum in rolling and rotating systems
Chapter 12

Static Equilibrium and Rigid-Body Applications

5 lessons
Conditions for translational and rotational equilibrium
Center of mass and support geometry
Beams, ladders, and suspended rigid bodies
Stability, tipping, and balance criteria
Engineering-style modeling of rigid-body systems
Chapter 13

Oscillations and Linearized Motion

6 lessons
Simple harmonic motion from Newton's second law
Energy methods for oscillatory systems
Angular frequency, phase, and amplitude
Small-angle approximations and rotational oscillations
Linearization near equilibrium points
Connections between circular motion and sinusoidal motion
Chapter 14

Integrated Translational and Rotational Systems

5 lessons
Rolling objects on inclines
Pulley systems with rotational inertia
Energy, momentum, and torque in multi-stage problems
Strategy selection across force, energy, and momentum methods
Multi-concept synthesis problems
Chapter 15

Advanced Problem Solving and Physical Modeling

6 lessons
Identifying the right model from physical information
Comparing exact, approximate, and numerical solutions
Dimensional analysis and scaling arguments
Interpreting real motion in laboratory and engineering contexts
Capstone applications in vehicles, sports, and machinery
Reflection: unifying translational and rotational mechanics