• Semester 3, position 2

-to provide students knowledge of the fundamental principles of Kinematics and Particle Dynamics -to enable students to master the determination of motion, properties of motion of mechanical objects and determination the causes of motions -to prepare students for solving the problems in different engineering and scientific fields

Upon successful completion of this course, students will be able to: • Analyze motion of a particle in various coordinate systems • Solve problems related to kinematics of a particle, i.e. to determine line of motion, trajectory, velocity, acceleration and sector velocity • Describe certain types of body motion: translation, rotation of a body about a fixed line, plane motion, spherical motion and general motion of a rigid body, as well as to determine kinematic quantities of a body (angular velocity and angular acceleration) and to determine velocity and acceleration of some points of a body • Solve kinematic problems related to the relative motion of a particle • Set differential equation related to the motion of a free and constrained particle, as well as to solve direct and inverse dynamic problem of a particle • Determine center of mass and inertia moments of a particle system and a rigid body

Basic Concepts of Kinematics. Determination of Motion of a Particle – Vector and Natural. Particle Velocity. Determination of Particle Velocity in Various Types of Coordinate Systems. Particle Acceleration. Determination of Particle Acceleration. Basic Terms of Kinematics of a Rigid Body. Translation. Rotation of a Rigid Body about a Fixed Axis. Angular Velocity and Angular Acceleration of a Rigid Body. Planar Kinematics of a Rigid Body. Spherical Kinematics of a Rigid Body. Relative Motion of a Particle. Velocity and Acceleration of a particle in Relative Motion. Free Particle Dynamics. Direct and Inverse Tasks of Dynamics. System of Particles. Constraints. Euler’s and Lagrange’s equations of Motion of a Particle. Center of Inertia. Moments of Inertia.

Determination of Motion of Particle – Vector and Natural. Determination of Particle Velocity in Various Types of Coordinate Systems. Determination of Particle Acceleration. Translation. Rotation of a Rigid Body about a Fixed Axis. Angular Velocity and Angular Acceleration of a Rigid Body. Planar Kinematics of a Rigid Body. Spherical Kinematics of a Rigid Body. Velocity and Acceleration of a Particle in Relative Motion. Free Particle Dynamics. System of Particles. Constraints. Euler’s and Lagrange’s equations of Motion of a Particle. Center of Inertia. Moments of Inertia.

Defined by curriculum.

[1] Mladenović, N., Mechanics 2, Kinematics, Faculty of Mechanical Engineering, Belgrade, 1996. [2] Simonović, M., Mitrović, Z., Golubović, Z., Mechanics - Kinematics, Faculty of Mechanical Engineering, Belgrade, 2011. [3] Mladenović, N., Mitrović, Z., Stokić, Z., Collections of examples for Kinematics, Faculty of Mechanical Engineering, Belgrade, 2007. [4] Mitrović, Z., Simonović, M., Golubović, Z., Mechanics - Dynamics of particle, Faculty of Mechanical Engineering, Belgrade, 2011. [5] Trišović, N., Lazarević, M., Practicum for Mechanics, Statics and Kinematics, Faculty of Mechanical Engineering, Belgrade, 1999. [6] Handouts

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 30
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 0
Test: 10
Final exam: 5

Activity during lectures: 0
Test/test: 60
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 40
Requirement for taking the exam (required number of points): 30

Rusov, L., Kinematics, Naučna knjiga, 1983.; Đurić, S., Kinematics, Faculty of Mechanical Engineering, Belgrade, 1990.; Pavišić, M., Stokić, Z., Trišović, N., Practicum for Mechanics, Particle Dynamics. Mechanical System Dynamics, Faculty of Mechanical Engineering, Belgrade,1998.