← Theoretical Mechanics

⇄ Sync
Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

Theory of all steps of the program by blocks. Open a topic to read it.

How a session goes

A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.

Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.

About the course

Statics: constraints and reactions, planar and spatial force systems, couples, distributed loads, trusses (method of joints, method of sections), friction. Kinematics of a point and a rigid body, plane motion and the instantaneous centre of velocity, compound motion of a point. Dynamics: d'Alembert's principle, virtual displacements, Lagrange's equations.

Course program: 34 lessons

Statics: forces and moments

  1. Axioms of statics, constraints and reactions
  2. Force projections and concurrent forces
  3. Moment of a force and couples
  4. Forces and moments: more
  5. Checkpoint: forces and moments

Equilibrium: beams and cantilevers

  1. Equilibrium conditions of a planar system
  2. Distributed loads
  3. Reactions of a simply supported beam
  4. Cantilever with a fixed support
  5. Beams and cantilevers: more
  6. Checkpoint: beam equilibrium

Trusses, friction, centre of gravity

  1. Trusses: method of joints
  2. Trusses: Ritter's method of sections
  3. Sliding friction and the angle of friction
  4. Spatial force systems
  5. Centroid of composite shapes
  6. Trusses and friction: more
  7. Checkpoint: trusses, friction, centre of gravity

Kinematics

  1. Kinematics of a point: ways to describe motion
  2. Tangential and normal acceleration
  3. Translation and rotation of a rigid body
  4. Plane motion of a body
  5. Instantaneous centre of zero velocity
  6. Compound motion of a point, Coriolis acceleration
  7. Kinematics: more
  8. Checkpoint: kinematics

Dynamics

  1. Differential equations of motion of a point
  2. d'Alembert's principle
  3. Work–energy theorem
  4. Dynamics: more
  5. Principle of virtual displacements
  6. Generalized coordinates and Lagrange's equations
  7. Analytical mechanics: more
  8. Checkpoint: dynamics