III.1.1. Reference system. Movement and rest

A body with dimensions negligible to the size of the displacements or to the distance at which other bodies are located can be represented by a point called the material point.

The mobile is a body that can move and is represented by a material point.

The landmark (reference body) is a body against which the position of another body is determined. It serves to spatially locate a body.

In the center of Bucharest, in front of the Church of St. George Nou, is located the monument that symbolically marks the place considered the starting point of all roads in our country - "zero kilometer". The monument Kilometer zero, was designed by architects Horia Creanga and Stefan Niculescu and materialized by the sculptor Constantin Baraschi in 1938. The monument at Kilometer 0 is a rose of the winds, between whose rays are engraved the names of the main Romanian historical provinces: Transylvania, Banat, Bassarabia , Bucovina, Dobrogea, Moldova, Muntenia and Oltenia.

Time measuring instruments (clock, stopwatch) are used for temporal location.

A body is in a state of motion when the body changes its position (or distance) from the chosen landmark.

A body is at rest when the body does not change its position (or distance) from the chosen landmark.

E.g:

You're in the physics lab, in the bank, in physics class. What mechanical condition are you in, moving or at rest?

If you choose as a landmark: the bench, the wall, the blackboard, etc. you are at rest, because you do not change your distance from these landmarks.

If you choose as a landmark: a traveler on the street, a bird flying out the window, the Sun, the Moon, etc. you are in a state of motion, because you change your distance from these landmarks.

We say that movement and rest are relative states, because they depend on the chosen landmark. So we can be in a certain moment of time both in motion and at rest depending on the chosen landmark.

But we cannot say about a body that it is both moving and at rest, at a certain moment and compared to the same landmark.

There is no absolutely fixed body (landmark) in the whole Universe, because there is no body at absolute rest. All bodies are moving relative to each other, because in reality, the chosen landmark is itself moving relative to other landmarks.

For example, I am resting in front of her in the car. But the car is moving against the road. The road moves towards the Earth with it. The earth moves toward its own axis and toward the Sun and other celestial bodies. Our solar system is moving toward our Galaxy, the Milky Way. Our galaxy is moving relative to the other galaxies in the universe.

But when we study the movement of a mobile with respect to a reference system (denoted SR), we consider its fixed landmark.

The trajectory is the line described by a mobile moving against a landmark (the line obtained by joining all the points that constitute the successive positions of the mobile).

Trajectory classification:

1. The rectilinear trajectory is a straight line.

Example:

• The trajectory of the car towards the ground;
• The movement of the plunger of a syringe relative to the syringe;
• The movement of a runner in the 100 meters race etc.

2. The curvilinear trajectory is a curved line.

Example:

• The trajectory of a ball thrown to the ground;
• The movement of a red lamp fixed on the wheel of the bicycle, etc.

3. The circular trajectory is a circle.

Example:

• The trajectory of a wheel relative to its axis (its center);
• The trajectory of a cabin in the amusement park in relation to its axis;
• The movement of a red lamp fixed on the wheel of the bicycle with respect to the axle, etc.

4. The point trajectory is a point: .

Example:

• The trajectory of any body towards itself.

🔓 Solved problems

1. You are on the seat of the bus that takes you to school. In what mechanical state (movement or rest) are you compared to:

a) The bus driver? I am at rest with the driver, because I do not change my position (distance) from him.

b) Bench? I'm at rest on the bench, because I'm not changing my position on it.

c) Earth? I am moving towards the Earth, because I am changing my distance from it.

d) Cars on the road? I am moving towards cars because I am changing my position towards them.

2. Draw the trajectories of a point on the wheel of your bicycle with respect to:

a) wheel axle (center).

The trajectory is circular (circle):

b) soil (Earth).

The trajectory is curvilinear: