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Theoretical questions. TP I
1. Define the position vector of the mass point. Explain the conception of position vector
differential in the appropriate figure. Describe its properties (magnitude, direction).
2. Define velocity of the mass point. Describe its properties. Define the acceleration of
the mass point. Express its velocity and acceleration in the component form.
3. Define the angular velocity and angular acceleration vectors. Draw their directions to
the figure. Derive the relation between peripheral and angular velocities.
4. Derive the relation for derivative of the unit vector.
5. Derive relations for tangential and normal accelerations.
6. Derive the equations describing uniformly straightforward and uniformly accelerated
motions of the mass point.
7. Define force momentum relative to a point. Explain its properties in the appropriate
figure.
8. Introduce the Newton laws of dynamics.
9. Introduce and explain the kinetic equation of the mass point.
10. Explain the terms of inertial and no inertial coordinate systems.
11. Define the force impulse and momentum of the mass point. Derive the relation
between the force impulse acting to the mass point and its momentum. Derive the law
of conservation of momentum of the mass point.
12. Define work acting to the mass point. Explain the term of the conservative force field.
Derive the relation for work of constant force.
13. Define kinetic energy of the mass point. Derive the relation between work of force
acting to the mass point and its kinetic energy change.
14. Define potential energy. Derive the principle of conservation of mechanical energy of
the mass point.
15. Introduce Newton gravitation law (gravitation force between two mass points). Draw
the sketch. Define intensity of the gravitation field.
16. Derive relation for potential energy of the mass point with mass of m in the gravitation
field with mass of M distant from it in the distance r.
17. Derive principle of the conservation of mechanical energy with mass of m in the
gravitation field with mass of M.
18. Define gravitation field potential. Derive relation between intensity and potential.
19. Describe gravitation field of the Earth. Derive principle of conservation of mechanical
energy of the mass point in the gravitation field near surface of the Earth (consider the
field to be homogeneous).
20. Define power and efficiency. Introduce their units.