Group of Chemical Physics

Responsible person: Marian Wittmann, associate professor, Dept. of Physics

2025/2026 Spring semester

Lecturer: István László Lagzi, associate professor, Dept. of Physics

GENERAL INFORMATION

Here is some information and requirements for the course (Mechanics for Chemical Engineers).

(i) Both lecture and practice will be held in person. However, you will find helpful information on Teams; therefore, please join the class online ASAP:

Általános | Mechanics - BMETE14AX15 (2025/2026) | Microsoft Teams

(ii) Lecture (room: CH307): MON 2:15-3:45 PM; Practice (room: CH304): TUE 2:15-3:45 PM. You must attend at least 70% of both lectures and practices.

(iii) There will be two (2) midterm exams. You can get a maximum of 20 points in each midterm. In the midterm exams, there will be NO theoretical questions and problems.

Midterm I: TBA

Midterm II: TBA

IMPORTANT: If you have a severe illness, injury, or circumstances that affect your ability to attend or complete the midterms, there will be two (2) replacement midterm exams. The first is free, and only one midterm exam/test can be replaced. The second one is paid; you can take two midterm exams/tests to fulfill the requirements. The date and time of the replacement exams will be announced later.

(iv) To fulfill the requirements for the practice (i.e., pass the practice), you should have at least 8 points out of 20 (maximum) points in two midterms (20 points (midterm I) + 20 points (midterm II) = 40 points).

(v) If you pass the practice (your course will be "signed" with no grade), you have the right to be admitted to the final exam in the exam period.

(vi) The final exam on the questions and problems will be written. The list of problems will be provided in the semester. The maximum number of points you can get in the final exam is 50.

(vii) During the semester, there will be two homework assignments (optional) for 5 points each.

(viii) Your final grade would be the composite from the points of midterms (max 40 points), homework (max 10 points), and final exam (max 50 points) as follows:

85.1-100.0: 5 (excellent)

70.1-85.0: 4 (good)

55.1-70.0: 3 (fair)

40.1-55.0: 2 (poor)

0 - 40: 1 (fail)

(viii) My contact: lagzi.istvan.laszlo@ttk.bme.hu; phone (office): +36-1463-1341
webpage: https://dept.physics.bme.hu/Self-organization

Recommended reading:

R. A. Serway – J. W. Jewett: Physics for Scientists and Engineers

A. Hudson – R. R. Nelson: University Physics

Detailed program of the subject:

LECTURES:

Introduction. Models, theories and laws. Units, standards, SI system. Reference frames. Coordinate systems. Vectors and scalars.

KINEMATICS: Motion in one dimension. Motion in two dimensions. Position vector. Average velocity, instantaneous velocity. Average acceleration, instantaneous acceleration. Position, velocity and acceleration in Cartesian and polar coordinates. Projectile motion. Circular motion. Curvilinear motion, tangential and radial accelerations.

THE LAWS OF MOTION: Inertial frames. Newton's laws. Force, mass. Normal force, tension, spring force, gravitational force, static and kinetic friction. Free body diagrams. The 1st cosmic speed.

WORK AND ENERGY: Work of a varying force. Kinetic energy and the work-energy theorem. Power.

POTENTIAL ENERGY: Work done by a spring. Work done by gravity. Work done by kinetic friction. Conservative and non-conservative forces. Potential energy. Conservation of mechanical energy. Changes in mechanical energy in the presence of non-conservative forces. Energy diagrams and the equilibrium of a system. The 2nd cosmic speed.

LINEAR MOMENTUM AND COLLISIONS: Linear momentum. Conservation of momentum. Elastic and inelastic collisions in 1D, 2D and 3D. Center of mass. Rocket propulsion.

ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS: Angular velocity vector, angular acceleration vector. Rotational kinetic energy. Moment of inertia. The parallel axis theorem. Torque. Work, power, energy.

ANGULAR MOMENTUM: Angular momentum of a particle and a system of particles. Conservation of angular momentum. Gyroscopes. Analogy between translational and rotation motion.

KEPLER'S LAWS OF PLANETARY MOTION.

STATIC EQUILIBRIUM: Conditions of equilibrium for a rigid object.

ACCELERATING FRAMES: Inertia forces: the translational inertia force, the centrifugal force, the Coriolis force, the Euler force. Discussion of motion in the rotating frame of the Earth.

OSCILLATORY MOTION: Simple harmonic motion, amplitude, phase constant, angular frequency. Mass attached to a spring. Energy of a simple harmonic oscillator. The simple pendulum. The physical pendulum. The torsional pendulum. Damped oscillations. Forced oscillations. Resonance.

BASICS OF CONTINUUM MECHANICS. Elastic properties of solids. Stress and strain, Young’s modulus, shear modulus, bulk modulus.  Pressure.  Fluids at rest, hydrostatic pressure. Pascal’s principle. Bouyant forces and Archimedes’ principle. Fluid dynamics. Flow rate and equations of continuity. Laminar flow. Bernoulli’s equation. Viscosity. Turbulent flow. Drag force. Dynamical lift.

PROBLEM SOLVING:

1. Vectors, functions. Choosing a reference frame.

2. Kinematics: position, displacement, velocity, acceleration in Cartesian coordinates.

3. Dynamics: projectile motion.

4. Normal force, tension, spring force, gravitational force, static and kinetic friction.

5. Circular motion in horizontal and vertical plane.

6. Center of mass. Conservation of momentum; elastic and inelastic collisions.

7. Harmonic oscillations. Drag force.

8. Work of a varying force. Conservative forces, potential energy.

9. The work-energy theorem. Conservation of mechanical energy.

10. Moment of inertia, the parallel axis theorem. Torque. Conservation of angular momentum.

Rotating and rolling motion.