Mechanics

1. apply the equilibrium conditions and determine unknown forces and reactions from the equilibrium conditions.
2. explain the phenomenon of friction. To be able to solve technical problems of equilibrium with the friction elements.
3. analyze the internal forces in the cross section of the beams and frames.
4. calculate the moments of inertia of the composite areas.
5. use the equations for position, velocity and acceleration of a particle for rectilinear and curvilinear motion in rectangular, polar and intrinsic coordinate systems.
6. apply the Newton’s second low of motion for particles, system of particles and rigid bodies.
7. calculate work of a force, power, kinetic energy, potential energy, linear momentum, angular momentum and linear impulse.
8. apply the low of conservation of energy, principle of work and energy, principle of impulse and momentum for particles, system of particles and rigid bodies.
9. solve problems with direct and oblique central impacts.

Lectures will be held in a block of three hours with examples and instructions for solving engineering problems.

The examples will be solved with students' active participation.

1. Lectures: Force, moment of force, force couple. Three-dimensional system of forces. Reduction to a simple form. Exercises: Determination of resultant force. Determination of moment of force. Examples of force reduction.
2. Lectures: Free body isolation principle. Body connections and contacts. Free body diagram. Exercises: Examples of free body diagrams.
3. Lectures: Equilibrium. Conditions and equations of equilibrium. Exercises: Examples of analytical conditions of equilibrium.
4. Lectures: Friction force. Friction on inclined plane. Belt friction. Exercises: Examples of equilibrium conditions of force systems with friction forces. Examples of equilibrium conditions of systems with belt friction.
5. Lectures: Analysis of internal forces. Simple beams and frames. Exercises: Diagrams of internal forces of simple beams and frames.
6. Lectures: Definition of center of gravity. Center of gravity of a composite body. Moments of inertia of areas. Exercises: Determination of center of gravity. Determination of moments of inertia of areas.
7. Lectures: Trajectory, velocity, acceleration. Straight line motion. Curvilinear motion in several coordinate systems. Exercises: Examples for straight line motion. Curvilinear motion examples.
8. Lectures: Intristic coordinate system. Translation of a rigid body. Rotation about fixed axis. Planar motion of a rigid body. Exercises: Curvilinear motion examples. Examples of rigid body rotation about stationary axis and planar motion.
9. Lectures: Planar motion of a rigid body: velocity and acceleration diagram. Kinematics of a relative motion. Exercises: Examples for velocity and acceleration diagram. Examples in relative motion of a point.
10. Lectures: Equation of motion of a particle. The principle of d'Alembert. Work and power. Kinetic energy and kinetic energy law. Exercises: Examples for equation of motion of a particle and principle of dAlembert. Examples for kinetic energy laws.
11. Lectures: Potential energy. Energy conservation principle. Linear impulse and linear momentum. Linear impulse and momentum principle. Exercises: Examples for potential energy laws. Energy conservation principle. Linear impulse and linear momentum. Linear impulse and momentum principle.
12. Lectures: Angular momentum and principle of angular impulse and angular momentum principle. Basics laws of motion for system of particles. Exercises: Motion under central force action. Examples illustrating system of particles dynamics.
13. Lectures: Rigid body dynamics: translation, rotation about fixed axis. Exercises: Examples of rotation about fixed axis of rigid body.
14. Lectures: Planar motion dynamics, equation of motion. Exercises: Examples for planar motion dynamics.
15. Lectures: Collision of particles. Collision of particles and rigid body. Exercises: Examples for collision of particles.