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 will consider the laws of mechanics in physics, focusing on the dynamics of the translational and rotational movement of bodies.
Historical background
How and why bodies move has been of interest to 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 rest.
With the advent of the New Age, many scientists began to study the laws of motion in mechanics. It should be noted such names as Huygens, Hooke 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, authored byEnglishman Isaac Newton. In his scientific work, he clearly formulated the basic laws of motion of bodies in space, which, together with the law of universal gravitation, 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, in contrast to relativistic, the postulates of which were set forth in the early 20th century by Albert Einstein. In the first, there are only three main laws on the basis of which the entire branch of physics is based. They are called like this:
- 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 derived from them, however, no theoretical principle leads to any of them. These laws follow exclusively from numerous observations and experiments. Their validity is confirmed by the reliability of the predictions obtained with the help of them in solving various problems in practice.
Inertia law
Newton's first law in mechanics says that any body in the absence of external influence on it will maintain a state of rest or rectilinear motion in any inertial frame of reference.
To understand this law, one must understand the reporting system. It is called inertial only if it satisfies the stated law. In other words, in the inertial system there is nothere are fictitious forces that would be felt by observers. For example, a system moving uniformly and in a straight line can be considered inertial. On the other hand, a system that rotates uniformly about an axis is non-inertial due to the presence of 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 an external force. Note that several forces can act on the body. In this case, they must be added 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 motion of a body and its state of rest.
Newton's Second Law
He says that the reason for changing the nature of the movement of the body in space is the presence of an external non-zero force applied to it. In fact, this law is a continuation of the previous one. Its mathematical notation is as follows:
F¯=ma¯.
Here, the quantity a¯ is the acceleration, which describes the rate of change of the velocity vector, m is the inertial mass of the body. Since m is always greater than zero, the force and acceleration vectors point in the same direction.
The considered law is applicable to a huge number of phenomena in mechanics, for example, to the description of the process of free fall, movement with the acceleration of a car, sliding of a bar along an inclined plane, oscillation of a pendulum,tension of spring scales and so on. It is safe to say that it is the main law of dynamics.
Momentum and Momentum
If you turn directly to Newton's scientific work, you can see that the scientist himself formulated the second law of mechanics somewhat differently:
Fdt=dp, where p=mv.
The value p is called the momentum. Many mistakenly call it the impulse of the body. The amount of motion is an inertial-energy characteristic equal to the product of the body's mass and its speed.
Change the momentum by some value dp can only be done by an external force F acting on the body during the time interval dt. The product of a force and the time of its action is called the impulse of the force or simply the impulse.
When two bodies collide, a collision force acts between them, which changes the momentum of each body, however, since this force is internal with respect to the system of two bodies 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.
Spin with acceleration
If the law of mechanics formulated by Newton is applied to the motion of rotation, then the following expression will be obtained:
M=Iα.
Here M - angular momentum - this is a value that shows the ability of the force to make a turn in the system. The moment of force is calculated as the product of the vector force and the radius vector directed from the axis toapplication point. The quantity 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 value α is the angular acceleration, which allows you to determine how many radians per second the angular velocity changes.
If you carefully look at the written equation and draw an analogy between its values and indicators from the second Newtonian law, then we will get their complete 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 form, then the third law is the original brainchild of the great Englishman. So, it says: if two bodies come into force contact, then the forces acting between them are equal in magnitude and opposite in direction. More briefly, we can say that any action causes a reaction.
F12¯=-F21¯.
Here F12¯ and F21¯ - acting from the side of the 1st body to the 2nd and from the side of the 2nd to 1st strength, respectively.
There are many examples that confirm this law. For example, during a jump, a person is repelled from the surface of the earth, the latter pushes him up. The same goes for walking a walker and pushing off a swimmer's pool wall. Another example, if you press your hand on the table, then the opposite is felt.the effect of the table on the hand, which is called the reaction force of the support.
When solving problems on the application of Newton's third law, one should not forget that the action force and the reaction force are applied to different bodies, therefore they give them different accelerations.
