The movement of different bodies in space in physics is studied by a special section - mechanics. The latter, in turn, is divided into kinematics and dynamics. In this article, we consider the laws of mechanics in physics, focusing on the dynamics of translational and rotational movement of bodies.
Historical reference
How and why bodies move, have been interested in philosophers and scientists since ancient times. So Aristotle believed that objects move in space only because there is some external influence on them. If this effect is stopped, the body will immediately stop. Many ancient Greek philosophers believed that the natural state of all bodies is peace.
With the advent of modern times, many scientists began to study the laws of motion in mechanics. It should be noted such surnames as Huygens, Guk and Galileo. The latter developed a scientific approach to the study of natural phenomena and, in fact, discovered the first law of mechanics, which, however, does not bear his last name.
In 1687, a scientific publication was published, the author of which was the Englishman Isaac Newton. In his scientific work, he clearly formulated the basic laws of the motion of bodies in space, which, together with the law of gravity, formed the basis not only of mechanics, but of all modern classical physics.
About Newton's Laws
They are also called the laws of classical mechanics as opposed to relativistic, the postulates of which were stated at the beginning of the 20th century by Albert Einstein. In the first, there are only three main laws on the basis of which the whole branch of physics is based. They are called like this:
- The law of inertia.
- The law of the relationship between force and acceleration.
- The law of action and reaction.
Why are these three laws the main ones? It's simple, any formula of mechanics can be obtained on their basis, however, not a single theoretical principle leads to any of them. The named laws follow solely from numerous observations and experiments. Their validity is confirmed by the reliability of the predictions obtained with their help in solving various problems in practice.
Inertia law
Newton's first law in mechanics says that every body in the absence of external influence on it will maintain a state of rest or rectilinear motion in any inertial system of the report.
To understand this law, you should deal with the reporting system. It is called inertial only if it satisfies the above law. In other words, in the inertial system there are no fictitious forces that the observers would sense. For example, a system moving uniformly and in a straight line can be considered inertial. On the other hand, a system that rotates uniformly around an axis is non-inertial due to the presence of a fictitious centrifugal force in it.
The law of inertia establishes the reason why the nature of the movement changes. This reason is the presence of external force. Note that several forces can act on the body. In this case, they must be folded according to the rule of vectors, if the resulting force is equal to zero, then the body will continue its uniform motion. It is also important to understand that in classical mechanics there is no difference between the uniform movement of the body and its state of rest.
Second Newton's Law
He says that the reason for the change in the nature of the movement of the body in space is the presence of an external nonzero force applied to it. In fact, this law is a continuation of the previous one. His mathematical record is as follows:
F¯ = m * a¯.
Here, the quantity a¯ is the acceleration describing the rate of change of the velocity vector, and m is the inertial mass of the body. Since m is always greater than zero, the force and acceleration vectors are directed in the same direction.
The law in question is applicable to a huge number of phenomena in mechanics, for example, to a description of the free fall process, movement with acceleration of a car, slipping of a bar along an inclined plane, oscillation of a pendulum, stretching of spring weights and so on. It is safe to say that it is the main law of dynamics.
Momentum and momentum
If we turn directly to the scientific work of Newton, we can see that the scientist himself formulated the second law of mechanics somewhat differently:
F * dt = dp, where p = m * v.
The value of p is called the momentum. Many mistakenly call it the impulse of the body. The momentum is an inertial-energy characteristic equal to the product of body mass and its speed.
Only the external force F acting on the body during the time interval dt can change the momentum by a certain value dp. The product of a force for the duration of its action is called a momentum of force or simply an impulse.
When two bodies collide, a collision force acts between them, which changes the momentum of each body, however, since this force is internal to the two-body system under study, it does not lead to a change in the total momentum of the system. This fact is called the law of conservation of momentum.
Acceleration rotation
If the law of mechanics formulated by Newton is applied to the motion of rotation, we obtain the following expression:
M = I * α.
Here M is the angular momentum - this is a quantity that shows the possibility of force to make a turn in the system. The moment of force is calculated as the product of a vector force by a radius vector directed from the axis to the point of application. The value of I is the moment of inertia. Like the moment of force, it depends on the parameters of the rotating system, in particular, on the geometric distribution of body mass relative to the axis. Finally, the quantity α is the angular acceleration, which allows one to determine how many radians per second the angular velocity changes.
If we carefully look at the written equation and draw an analogy between its values and indicators from the second Newtonian law, we will get their full identity.
The law of action and reaction
It remains for us to consider the third law of mechanics. If the first two, one way or another, were formulated by Newton's predecessors, and the scientist himself only gave them a harmonious mathematical appearance, then the third law is the original brainchild of the great Englishman. So, he says: if two bodies come into force contact, then the forces acting between them are equal in magnitude and opposite in direction. More briefly, one can say that any action causes a reaction.
F 12 ¯ = -F 21 ¯.
Here F 12 ¯ and F 21 ¯ are acting from the side of the 1st body to the 2nd and from the side of the 2nd to the 1st force, respectively.
There are many examples supporting this law. For example, during a jump a person pushes off the surface of the earth, the latter pushes him up. The same goes for pedestrian walking and pushing away from the swimmer's pool wall. Another example, if you put your hand on the table, you feel the opposite effect of the table on the hand, which is called the reaction force of the support.
When solving the problems of applying the third Newtonian law, one should not forget that the force of action and the force of reaction are applied to different bodies, therefore they are informed of different accelerations.