Entry requirements

Participation in Algebra and Geometry

Learning outcomes

On completion of the course the student shall be able to:

• use vector algebra in three dimensions in different bases, length, addition and multiplication of vectors, inner product, cross product, for calculations in mechanics.
• use properties of the inner product and the cross product, geometric and physical interpretations, differentiation of vector functions, differentiation of coordinates and basis vectors in different coordinate systems, for calculations in mechanics.
• use vectors to describe geometric quantities as curves, area and volume elements, as well as physical quantities as velocity, acceleration, force and torque.
• describe and explain fundamental quantities in kinematics and dynamics of particles and particle systems in inertial and non-inertial systems.
• explain and use the theory of classical mechanics, consisting of relations between the fundamental quantities based on Newton's laws, in simple given examples.
• apply the fundamental quantities and the theory of classical mechanics by analysing physical processes and construct mathematical models for statics and dynamics of objects.
• show analytical problem solving skills for mechanical and engineering applications and account for relevant approximations.
• carry out physical experiments and present, explain and defend the results.

Content

Geometry, trigonometry and vector algebra: vector algebra in three dimensions using different bases, length, addition and multiplication of vectors, inner product and cross product. The properties of the inner product and the vector product, geometric and physical interpretations, rules of differentiation for vector functions, differentiation of coordinates and basis vectors in different coordinate systems. Curves, area elements, volume elements.

Applications of statics and geometry: force, torque.

The kinematics of particles in different coordinate systems, cartesian-, normal and tangential- as well as polar coordinates.

The dynamics of particles: force, linear momentum, impulse, torque, angular momentum, angular impulse, Newton's laws.

Particle systems, center of mass, Euler's law for the movement of the the center of mass. Mass flows, the rocket equation.

Work and energy. Energy relations. Gradient.

Accelerated reference frames.

The development of the mechanics. Kepler's laws. Short introduction to oscillatory motion.

Models for the motion of objects with applications.

Experimental work, laboratory exercises, oral and written reports.

Instruction

Lectures, exercise classes, group work and laboratory exercises. Guest lecture or study visit.

Assessment

Written examination at the end of the course as well as optional written continuous examination that can substitute parts of examination (8 credits). Laboratory exercises with oral and written presentations (2 credits).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course may not be included in a degree together with one of the courses Mechanics I 1FA101 or Mechanics 1FA104.