Laws of dynamics

The section of mechanics that studies the movement of a body under the influence of forces applied to it is called dynamics. A classic is called the dynamics, which is based on the laws of Newton. He in 1687 formulated the basic laws of dynamics. It is about them that will be discussed in our article.

Law of inertia

This is the first law of dynamics, describing the simplest mechanical movement of a material point in the conditions of its complete isolation from the influence of other material objects.

This law states that any isolated material point, that is, such a point that is not influenced by other material bodies, can perform with respect to any fixed frame only a uniform rectilinear motion (the speed in this case is a constant value) or be at rest (speed is zero).

The property of a material point to keep the state of motion unchanged, in the absence of forces acting on it, or they are in equilibrium, is called the inertia of this point. Inertial or basic is called the reference system in respect of which the law of inertia is valid. And absolute motion is called motion relative to this system.

An inertial is also any other frame of reference, which moves in relation to this inertial system in a straight line, translationally, uniformly. A system that is still connected to the Earth is also mistaken for an inertial system. The truth is that this is done with an approximation that is sufficient for practical solutions.

Second law

Continuing to study the laws of dynamics, we consider the second law, which is called the basic law of dynamics. The violation of the inertial state of a material point, that is, the appearance of its acceleration, occurs under the influence of other material objects or points on it. This effect is characterized by a vector quantity called the force applied to this point.

Power characteristics:

  • The direction of impact on the material point from the side of another body or point.
  • The intensity of the impact on the point and the dependence of its acceleration on the resistance to this impact.

The ability of a material point to resist a change in uniform rectilinear motion or a state of rest is inertness. Its measure is mass, m.

The second basic law of dynamics suggests that the force that acts on a material point is proportional to the mass of this point and to the acceleration that is imparted to the point by the force applied to it.

F = kmw, where the F-vector of the applied force, the m-mass of the body, the w-vector of acceleration and the k-coefficient of proportionality.

If the proportionality factor is taken as 1, then the basic law of dynamics will be expressed as:

F = mw, where w is the absolute acceleration of the body, that is, acceleration with respect to some inertial CO.

From this it follows that we can determine the mass of a point on the basis of the acceleration, which was obtained by it under the influence of a known force. Acceleration of free fall near the Earth is a constant value. The force that informs the body of this acceleration is called weight. From here, the notion of a weighty mass will follow.

Third law

The law of equality of counteraction and action is also an axiom of statics. This law says that the forces of interaction of two material points act in the direction of one straight line. They are directed oppositely and numerically equal to each other, that is, F12 = F21.

If the forces are represented as F12 = m1w1 and F21 = m2w2, then since F12 = F21, then we get that m1w1 = m2w2, it follows that w1 / w2 = m1 / m2. This means that the accelerations, or rather their modules, communicated to each other by material bodies as they interact, will be inversely proportional to the masses of these bodies.

Fourth law

We have not yet considered all the laws of dynamics. Consider the fourth law, the law of independence of action of forces. He says that a material body under the influence of several forces will receive an acceleration that will be equal to the geometric sum of the accelerations that it will receive from each force. These forces operate separately and independently from each other.

Thus, the system of forces that were applied to a single material body would be equivalent to one resultant force, which is equal to the main vector of the entire system of forces. Be sure to pay attention to the fact that the basic laws of Newton's dynamics can be considered only in close relationship with each other. In this case, they are the foundation of dynamics - a science that describes mechanical motion, ascertaining the causes of changes in the velocities of objects, explaining and controlling this motion.