DYNAMICS OF TRANSLATIONAL MOTION

 

§ 1 Newton's first law.
Inertial reference system


 Newton's 1 law: Every body is at rest or in uniform motion as long as the effects of other bodies do not bring it out of this state

 -  Newton's 1 law

 

This law is called the law of inertia. Inertia - the body's ability to maintain speed. Inertial motion - motion with constant velocity.
 Newton's 1 law holds not in all frames. Reference frame in which the 1-Newton's law is
valid, called inertial. Any system, moving relative to an inertial system uniformly, will also inertial.

An example of an inertial reference frame can serve as the heliocentric reference frame, i.e., the reference frame of the Sun.

Any system, moving relative to the heliocentric uniform rectilinear will be inertial.
The laboratory frame, the axes of which are rigidly connected to the Earth, is not inertial, because of non-inertial rotation of the earth. However, the Earth's rotation is very slow, with a = 0.034 m/s2, and so in most applications laboratory frame of reference can be considered as approximately inertial.

The content of the 1st Newton's law reduced to two statements:
1) all have the property of inertia of the body;

2) there are inertial frames of reference.
Inertial reference systems play a special role not only in mechanics, but also in other areas of physics, because the principle of relativity Einstein's mathematical notation of any physical law must have the same form in all inertial reference frames.

 

§ 2 Mass, momentum of the body.
2nd law of Newton


The same effect in different ways alters the movement of various bodies. When exposed to any body changes its velocity at once, but gradually. The body's ability to maintain its speed is called inertia. The measure of inertia is mass. Body mass - a positive scalar value, a measure of inertia of a body, that is characterized by the body's ability to maintain its speed.

Under the action of the body changes its velocity is not instantaneous, but gradually, i.e., acquires a finite acceleration, which is smaller, the greater the mass, that is, when exposed to the same forces

 

Density is the ratio of body mass dm small volume dV to the value of this volume

,

if the body is homogeneous, then ρ = const and

Center of mass, or center of mass system of particles is a point with a radius vector , which is equal to

 

Vector quantity  equal to the mass m of a point on its velocity is called momentum (or linear momentum) of the material point

Momentum of the system is the vector of point , equal to the geometric sum (ie, the sum of the vectors) of all material points

Velocity of the center of inertia:

that is, the momentum of the system is equal to the mass of the entire system on the speed of its center of inertia.


2nd Newton's law: the rate of change of momentum of the body is acting on the body force F

If the body has several forces, under the force F in Newton's second law is necessary to understand the resultant force (net force) - geometrical sum of all forces acting on the body.
From Newton's second law, it follows that

Vector quantity Fdt called the elementary impulse of forcer.
Impulse, for a finite time interval t2 - t1 is

where

 - 2-nd Newton's law –

the basic equation of the dynamics of the translational motion of a rigid body. The force acting on a body is equal to the mass of the body to its acceleration.


Tangent and normal acceleration determined by the appropriate component of the force F

      

        

Force Fn, which imparts at normal acceleration is directed towards the center of curvature of the trajectory and is therefore called the centripetal force.

 

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