How can I understand mechanics

3.1 Kinematics and kinetics

  1. How is the velocity vector defined?
  2. How is the acceleration vector defined?
  3. How are the velocity vector and the acceleration vector calculated based on a known position vector as a function of time?
  4. How do you calculate the magnitude of the speed vector if the coordinates of this speed vector in a Cartesian coordinate system are known?
  5. Explain the term trajectory with the help of a sketch. Represent the corresponding position vector using a Cartesian coordinate system.
  6. What is meant by the initial conditions of the movement of a point on the body?
  7. In addition to the Cartesian coordinate system, why is e.g. also uses the polar coordinate system?
  8. What is the fundamental difference between the unit vectors of a Cartesian coordinate system and a polar coordinate system?
  9. Explain the terms angular velocity and angular acceleration!
  10. Explain the terms relative movement and absolute movement using an example.
  11. What is a Coriolis acceleration? Under what conditions does this occur?

3.2 Rigid Body Kinematics

  1. How do you calculate the speed and acceleration of a point on a rigid body that rotates around a fixed axis?
  2. How do you calculate the velocity of any point on a rigid body if the velocity of a particular point and the angular velocity of the rigid body are known? Answer the question with the help of a sketch.
  3. What is the relationship between the speed and the angular velocity of a shaft? When answering the question, include the units of measurement.
  4. What do you understand by the momentary pole of the velocities in the plane movement of a rigid body?
  5. Which statement can you make regarding the speed of a point at a distance r from the instantaneous pole?

3.3 Rigid Body Kinetics

  1. What do you understand by the d'Alembertian mass forces and how is their sense of direction defined?
  2. How do you determine the frictional force between two bodies sliding on each other?
  3. A body moves in translation as a result of the action of an external force. Give an example for a constant force, one depending on the position of the body and one depending on the speed of the body in force.
  4. What do you understand by the terms momentum, angular momentum, kinetic energy, work and power? Use formulas to answer the questions.
  5. Explain the momentum and the law of conservation of momentum for rigid bodies in translations.
  6. How do you calculate the work of a constant force that moves a body in a straight line?
  7. What is the potential energy of a linear spring with the spring constant c, which is compressed in order to move it out of the relaxed position?
  8. What can be said about the force in a body if the work proves to be independent of the path?
  9. How is the moment of inertia of a rigid body defined that rotates around an axis fixed in space?
  10. How can you calculate the moment of inertia in relation to an axis that is parallel to the axis of the center of gravity, if you use the moment of inertia in relation to the axis of the center of gravity?
  11. How many degrees of freedom does a rigid body have that can only move in a plane?
  12. How do you calculate the power of a moment that turns a rigid body rotating around a fixed axis with the angular velocity omega?
  13. Which methods for setting up the equation of motion of a system with degree of freedom 1 do you know?
  14. When is the application of the impulse theorem and when the application of the working theorem advantageous when solving dynamic problems?

3.5 Oscillations with the degree of freedom 1

  1. What do you understand by a vibration in general and what specifically by a harmonic vibration?
  2. Explain the terms angular frequency, frequency, period of oscillation, zero phase angle and amplitude for a harmonic oscillation!
  3. What kind of movement occurs when two harmonic vibrations are superimposed, their circular frequencies
  4. a) are equal, b) are in a rational relationship, c) form a relationship that represents an irrational number?
  5. What kind of movement occurs when two harmonic oscillations are superimposed whose circular frequencies differ only slightly from one another?
  6. On which parameters does the natural frequency of an oscillator with one degree of freedom depend?
  7. What are the relationships between the natural angular frequency Omega, the natural frequency f and the period of oscillation T?
  8. What does the amplitude of the free oscillation of a system with one degree of freedom depend on?
  9. How is the period of oscillation of a spring-mass system calculated?
  10. Do you sketch the course of a damped oscillation and describe the characteristic quantities?
  11. When do we speak of a forced oscillation? What possibilities of arousal are there? Give two examples in this regard.
  12. At which frequency does a harmonically excited, linear oscillator oscillate in the steady state?
  13. Explain the term magnification function!
  14. Explain the term resonance!
  15. On which parameters does the amplitude of the forced oscillation depend?
  16. What is meant by the term voting ratio?

3.6 Shock processes

  1. What is the difference between a straight and an oblique push?
  2. What is a centric and what is an eccentric shock?
  3. Explain the collision phases using a straight, centric collision between two bodies.
  4. Which physical quantity is retained when two bodies collide?
  5. What is meant by the collision number k? What does k = 1 and what does k = 0 mean?

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