Forces acting on any point mechanical system, are divided into internal and external.
Fi– inner strength
Fe– external force
Internal are called the forces with which the points included in the system act on each other.
External are called forces that are applied to points from the outside, that is, from other points or bodies not included in the system. The division of forces into internal and external is conditional.
mg – external force
Ftr – internal strength
Mechanical system. External and internal forces.
A mechanical system of material points or bodies is a collection of them in which the position or movement of each point (or body) depends on the position and movement of all the others.
We will also consider a material absolutely solid body as a system of material points that form this body and are interconnected in such a way that the distances between them do not change and remain constant all the time.
A classic example of a mechanical system is the solar system, in which all bodies are connected by forces of mutual attraction. Another example of a mechanical system is any machine or mechanism in which all the bodies are connected by hinges, rods, cables, belts, etc. (i.e. various geometric connections). In this case, the bodies of the system are subject to mutual pressure or tension forces transmitted through connections.
A collection of bodies between which there are no interaction forces (for example, a group of airplanes flying in the air) does not form a mechanical system.
In accordance with what has been said, the forces acting on points or bodies of the system can be divided into external and internal.
External forces are those acting on points of a system from points or bodies that are not part of the given system.
Internal forces are those acting on points of a system from other points or bodies of the same system. We will denote external forces by the symbol - , and internal forces by - .
Both external and internal forces can, in turn, be either active or reactions of connections.
Reactions of connections, or simply reactions, are forces that limit the movement of points in the system (their coordinates, speed, etc.). In statics these were forces replacing connections. In dynamics, a more general definition is introduced for them.
Active or given forces are called all other forces, everything except reactions.
The necessity of this classification of forces will become clear in the following chapters.
The division of forces into external and internal is conditional and depends on the movement of which system of bodies we are considering. For example, if we consider the movement of the entire solar system in general, the force of attraction of the Earth to the Sun will be internal; when studying the movement of the Earth in its orbit around the Sun, the same force will be considered as external.
Internal forces have the following properties:
1. The geometric sum (principal vector) of all internal forces F12 and F21 of the system is equal to zero. In fact, according to the third law of dynamics, any two points of the system (Fig. 31) act on each other with equal in magnitude and oppositely directed forces and, the sum of which is equal to zero. Since a similar result holds for any pair of points in the system, then
2. Sum of moments ( main point) of all internal forces of the system relative to any center or axis is equal to zero. Indeed, if we take an arbitrary center O, then from Fig. 18 it is clear that . A similar result will be obtained when calculating the moments about the axis. Therefore, for the entire system there will be:
However, it does not follow from the proven properties that the internal forces are mutually balanced and do not affect the movement of the system, since these forces are applied to different material points or bodies and can cause mutual movements of these points or bodies. The internal forces will be balanced when the system under consideration is an absolutely rigid body.
30Theorem on the motion of the center of mass.
System weight equals the algebraic sum of the masses of all points or bodies of the system in a uniform gravitational field, for which the weight of any particle of the body is proportional to its mass. Therefore, the distribution of masses in a body can be determined by the position of its center of gravity - geometric point C, the coordinates of which are called the center of mass or center of inertia of a mechanical system
Theorem on the motion of the center of mass of a mechanical system : the center of mass of a mechanical system moves as a material point whose mass is equal to the mass of the system, and to which all external forces acting on the system are applied
Conclusions:
A mechanical system or a rigid body can be considered as a material point depending on the nature of its motion, and not on its size.
Internal forces are not taken into account by the theorem on the motion of the center of mass.
The theorem on the motion of the center of mass does not characterize rotational movement mechanical system, but only translational
Law on the conservation of motion of the center of mass of the system:
1. If the sum of external forces (the main vector) is constantly equal to zero, then the center of mass of the mechanical system is at rest or moves uniformly and rectilinearly.
2. If the sum of the projections of all external forces onto any axis is equal to zero, then the projection of the velocity of the center of mass of the system onto the same axis is a constant value.
The equation expresses the theorem on the motion of the center of mass of the system: the product of the mass of the system and the acceleration of its center of mass is equal to geometric sum all external forces acting on the system. Comparing with the equation of motion material point, we obtain another expression of the theorem: the center of mass of the system moves as a material point, the mass of which is equal to the mass of the entire system and to which all external forces acting on the system are applied.
If expression (2) is placed in (3), taking into account the fact that we get:
(4’) – expresses the theorem on the movement of the center of mass of the system: the center of mass of the system moves as a material point on which all the forces of the system act.
Conclusions:
1. Internal forces do not affect the movement of the center of mass of the system.
2. If , the movement of the center of mass of the system occurs at a constant speed.
3., then the movement of the center of mass of the system in projection onto the axis occurs at a constant speed.
These equations are differential equations movement of the center of mass in projections on the axis Cartesian system coordinates
The meaning of the proven theorem is as follows.
1) The theorem provides justification for the methods of point dynamics. From the equations it is clear that the solutions that we obtain by considering a given body as a material point determine the law of motion of the center of mass of this body, i.e. have a very specific meaning.
In particular, if a body moves translationally, then its motion is completely determined by the movement of the center of mass. Thus, a translationally moving body can always be considered as a material point with a mass equal to the mass of the body. In other cases, a body can be considered as a material point only when, practically, to determine the position of the body it is enough to know the position of its center of mass.
2) The theorem allows, when determining the law of motion of the center of mass of any system, to exclude from consideration all previously unknown internal forces. This is its practical value.
So the movement of the car horizontal plane can only occur under the influence of external forces, friction forces acting on the wheels from the road. And braking a car is also possible only with these forces, and not with friction between the brake pads and the brake drum. If the road is smooth, then no matter how much you brake the wheels, they will slide and will not stop the car.
Or after the explosion of a flying projectile (under the influence of internal forces), its parts, fragments, will scatter so that their center of mass will move along the same trajectory.
The theorem on the motion of the center of mass of a mechanical system should be used to solve problems of mechanics that require:
Using the forces applied to a mechanical system (most often to a solid body), determine the law of motion of the center of mass;
Based on the given law of motion of bodies included in a mechanical system, find the reactions external relations;
Based on the given mutual motion of bodies included in a mechanical system, determine the law of motion of these bodies relative to some fixed reference system.
Using this theorem, you can create one of the equations of motion of a mechanical system with several degrees of freedom.
When solving problems, corollaries from the theorem on the motion of the center of mass of a mechanical system are often used.
Corollary 1. If the main vector of external forces applied to a mechanical system is equal to zero, then the center of mass of the system is at rest or moves uniformly and rectilinearly. Since the acceleration of the center of mass is zero, .
Corollary 2. If the projection of the main vector of external forces onto any axis is zero, then the center of mass of the system either does not change its position relative to this axis or moves uniformly relative to it.
For example, if two forces begin to act on a body, forming a pair of forces (Fig. 38), then its center of mass C will move along the same trajectory. And the body itself will rotate around the center of mass. And it doesn’t matter where the couple of forces are applied.
External forces- these are forces acting on a body from the outside. Under the influence of external forces, a body either begins to move if it was at rest, or the speed of its movement or the direction of movement changes. External forces in most cases are balanced by other forces and their influence is invisible.
External forces acting on a solid body cause changes in its shape, caused by the movement of particles.
External forces:
- gravity - this is the force that acts on a body in a field gravity. On the surface of the earth, the force of gravity is equal to the mass of the body. It is always directed vertically downwards, perpendicular to the horizon. Dot applications - general center of gravity of the body.
-ground reaction force - this is the force acting on the body from the side of the support when there is pressure on it.
-friction force - this is the force that occurs during contact between bodies and during the movement of the body.
-environmental resistance force- a force that arises when a body moves in an air or water environment.
-inertial force - a force that occurs when a body moves with acceleration.
By internal forces are the forces acting between particles, these forces resist changing shape.
Internal forces are divided into active and passive.
Active forces include the force of contraction of skeletal muscles.
Muscle strength is determined by:
Physiological diameter,
Area of origin and attachment,
The type of lever in which the movement occurs.
Passive ones include: the force of elastic traction of soft tissues, the resistance force of cartilage, bones, the force of molecular adhesion of synovial fluid.
The concept of the general center of gravity of the body and the area of support. Their meaning.
GCT is composed of centers of gravity of individual parts of the body, and partial centers of gravity. It plays an important role in solving problems of mechanics of movement. It is one of the indicators of physique.
Support area- the area enclosed between the outer borders of the right and left foot. The size of the support area varies depending on the position of the body.
Types of body balance. The degree of stability of the body, its definition and meaning.
There are three types: stable (when the body’s central gravity is disturbed, the body’s central gravity increases and hangs on the crossbar), unstable (the central gravity of the body decreases), and indifferent (the central gravity of the body is constant).
The degree of stability depends on the height of the central center and the size of the support area. larger area supports and the lower the GCT, the higher the degree of stability.
The quantitative expression is the stability angle. This is the angle formed vertically by gravity and a tangent drawn to the edge of the support.
Characteristics of the athlete's movements. Types of movements. Examples.
In mechanics external forces in relation to a given system of material points (i.e. such a set of material points in which the movement of each point depends on the positions or movements of all other points) those forces are called that represent the action on this system of other bodies (other systems of material points) that we did not include in this system. Internal forces are the forces of interaction between individual material points of a given system. The division of forces into external and internal is completely conditional: when the given composition of the system changes, some forces that were previously external can become internal, and vice versa. So, for example, when considering
the movement of a system consisting of the earth and its satellite the moon, the interaction forces between these bodies will be internal forces for this system, and the gravitational forces of the sun, the remaining planets, their satellites and all the stars will be external forces in relation to the specified system. But if we change the composition of the system and consider the movement of the sun and all the planets as the movement of one common system, then external the forces will be only the forces of attraction exerted by the stars; nevertheless, the forces of interaction between the planets, their satellites and the sun become internal forces for this system. In the same way, if during the movement of a steam locomotive we single out the piston of the steam cylinder as a separate system of material points subject to our consideration, then the steam pressure on the piston in relation to it will be external force, and the same steam pressure will be one of the internal forces if we consider the movement of the entire locomotive as a whole; in this case, external forces in relation to the entire locomotive, taken as one system, will be: friction between the rails and wheels of the locomotive, gravity of the locomotive, reaction of the rails and air resistance; internal forces will be all the forces of interaction between parts of the locomotive, for example. interaction forces between steam and the cylinder piston, between the slider and its parallels, between the connecting rod and the crank pin, etc. As we see, there is essentially no difference between external and internal forces, the relative difference between them is determined only depending on which bodies we include in the system under consideration and which we consider not included in the system. However, the indicated relative difference in forces is very significant when studying the motion of a given system; according to Newton's third law (on the equality of action and reaction), the internal forces of interaction between each two material points of the system are equal in magnitude and directed along the same straight line in opposite sides; Thanks to this, when resolving various questions about the motion of a system of material points, it is possible to exclude all internal forces from the equations of motion of the system and thereby make possible the study of the motion of the entire system. This method of eliminating internal, in most cases unknown, coupling forces is essential in deriving various laws of mechanics of a system.
Absolutely elastic impact- a collision of two bodies, as a result of which no deformations remain in both bodies participating in the collision and all the kinetic energy of the bodies before the impact after the impact again turns into the original kinetic energy (note that this is an idealized case).
For absolutely elastic impact the law of conservation of kinetic energy and the law of conservation of momentum are satisfied.
Let us denote the velocities of the balls with masses m 1 and m 2 before impact through ν 1 And ν 2, after impact - through ν 1 " And ν 2"(Fig. 1). For a direct central impact, the velocity vectors of the balls before and after the impact lie on a straight line passing through their centers. The projections of the velocity vectors onto this line are equal to the velocity modules. We will take their directions into account using signs: positive ones will be associated with movement to the right, negative ones with movement to the left.
Fig.1
Under these assumptions, the conservation laws have the form
(1)
(2)
Having made the appropriate transformations in expressions (1) and (2), we obtain
(3)
(4)
Solving equations (3) and (5), we find
(7)
Let's look at a few examples.
1. When ν 2=0
(8) 
(9)
Let us analyze expressions (8) in (9) for two balls of different masses:
a) m 1 = m 2. If the second ball was hanging motionless before the impact ( ν 2=0) (Fig. 2), then after the impact the first ball will stop ( ν 1 "=0), and the second one will move with the same speed and in the same direction in which the first ball was moving before the impact ( ν 2"=ν 1);
Fig.2
b) m 1 >m 2. The first ball continues to move in the same direction as before the impact, but at a lower speed ( ν 1 "<ν 1). The speed of the second ball after impact is greater than the speed of the first ball after impact ( ν 2">ν 1 ") (Fig. 3);
Fig.3
c) m 1
Fig.4
d) m 2 >>m 1 (for example, a collision of a ball with a wall). From equations (8) and (9) it follows that ν 1 "= -ν 1; ν 2"≈ 2m 1 ν 2"/m 2 .
2. When m 1 =m 2 expressions (6) and (7) will have the form ν 1 "= ν 2; ν 2"= ν 1; that is, balls of equal mass seem to exchange velocities.
Absolutely inelastic impact- a collision of two bodies, as a result of which the bodies connect, moving further as a single whole. An absolutely inelastic impact can be demonstrated using plasticine (clay) balls that move towards each other (Fig. 5).
Fig.5
If the masses of the balls are m 1 and m 2, their velocities before impact ν 1 And ν 2, then, using the law of conservation of momentum
Where v- the speed of movement of the balls after impact. Then
(15.10)
If the balls move towards each other, they will together continue to move in the direction in which the ball moved with high momentum. In the particular case, if the masses of the balls are equal (m 1 =m 2), then
Let us determine how the kinetic energy of the balls changes during a central absolutely inelastic impact. Since during the collision of balls between them there are forces that depend on their velocities, and not on the deformations themselves, we are dealing with dissipative forces similar to friction forces, therefore the law of conservation of mechanical energy in this case should not be observed. Due to deformation, there is a decrease in kinetic energy, which turns into thermal or other forms of energy. This decrease can be determined by the difference in the kinetic energy of the bodies before and after the impact:
Using (10), we obtain
If the impacted body was initially motionless (ν 2 =0), then
When m 2 >>m 1 (mass stationary body very large), then ν <<ν 1 and practically all the kinetic energy of the body is converted into other forms of energy upon impact. Therefore, for example, to obtain significant deformation, the anvil must be significantly more massive than the hammer. On the contrary, when hammering nails into a wall, the mass of the hammer should be much greater (m 1 >>m 2), then ν≈ν 1 and almost all the energy is spent on moving the nail as much as possible, and not on residual deformation of the wall.
A completely inelastic impact is an example of the loss of mechanical energy under the influence of dissipative forces.
1. Work of variable force.
Let us consider a material point moving under the influence of force P in a straight line. If effective force is constant and directed along a straight line, and the displacement is equal to s, then, as is known from physics, the work A of this force is equal to the product Ps. Now let's derive a formula for calculating the work done by a variable force.
Let a point move along the Ox axis under the influence of a force, the projection of which onto the Ox axis is a function of f from x. In this case we will assume that f is continuous function. Under the influence of this force, the material point moved from point M (a) to point M (b) (Fig. 1, a). Let us show that in this case the work of A is calculated by the formula
(1)
Let's split the segment [a; b] into n segments of the same length. These are the segments [a; x 1 ], ,..., (Fig. 1.6). Work of force on the entire segment [a; b] is equal to the sum of the work done by this force on the resulting segments. Since f is a continuous function of x, for a sufficiently small segment [a; x 1 ] the work done by the force on this segment is approximately equal to f (a) (x 1 -a) (we neglect the fact that f changes on the segment). Similarly, the work done by the force on the second segment is approximately equal to f (x 1) (x 2 - x 1), etc.; the work done by the force on the nth segment is approximately equal to f (x n-1)(b - x n-1). Consequently, the work of force on the entire segment [a; b] is approximately equal to:
and the accuracy of the approximate equality is higher, the shorter the segments into which the segment [a;b] is divided. Naturally, this approximate equality becomes exact if we assume that n→∞:
Since A n tends to the integral of the function under consideration from a to b as n →∞, formula (1) is derived.
2. Power.
Power P is the rate of work done,
Here v is the speed of the material point to which the force is applied
All forces encountered in mechanics are usually divided into conservative and non-conservative.
A force acting on a material point is called conservative (potential) if the work done by this force depends only on the initial and final positions of the point. The work of a conservative force does not depend either on the type of trajectory or on the law of motion of a material point along the trajectory (see Fig. 2): 
.
Changing the direction of movement of a point along a small area to the opposite causes a change in sign basic work, hence, . Therefore, the work of a conservative force along a closed trajectory 1 a 2b 1 equals zero: 
.
Points 1 and 2, as well as sections of closed trajectory 1 a 2 and 2 b 1 can be chosen completely arbitrarily. Thus, the work of a conservative force along an arbitrary closed trajectory L of the point of its application is equal to zero:
In this formula, the circle on the integral sign shows that the integration is carried out along a closed path. Often a closed trajectory L called a closed loop L(Fig. 3). Usually specified by the direction of traversal of the contour L clockwise. The direction of the elementary displacement vector coincides with the direction of the contour traversal L. In this case, formula (5) states: vector circulation by closed loop L is zero.
It should be noted that the forces of gravity and elasticity are conservative, and the forces of friction are non-conservative. In fact, since the friction force is directed in the direction opposite to the displacement or speed, the work of the friction forces along a closed path is always negative and, therefore, not equal to zero.
Dissipative system(or dissipative structure, from lat. dissipatio- “disperse, destroy”) is an open system that operates far from thermodynamic equilibrium. In other words, this is a stable state that arises in a nonequilibrium environment under the condition of dissipation (dissipation) of energy that comes from outside. A dissipative system is sometimes also called stationary open system or nonequilibrium open system.
A dissipative system is characterized by the spontaneous appearance of a complex, often chaotic structure. Distinctive feature such systems - non-conservation of volume in phase space, that is, non-fulfillment of Liouville's Theorem.
A simple example Such a system is Benard cells. As more complex examples called lasers, the Belousov-Zhabotinsky reaction and biological life.
The term “dissipative structure” was introduced by Ilya Prigogine.
Recent research in the field of “dissipative structures” allows us to conclude that the process of “self-organization” occurs much faster in the presence of external and internal “noise” in the system. Thus, noise effects lead to an acceleration of the “self-organization” process.
the energy of a mechanical system, depending on the speed of movement of its points. K. e. T material point is measured by half the product of mass m this point by the square of its speed υ, i.e. T = 1/ 2 mυ 2 . K. e. mechanical system is equal to arithmetic sum K. e. all its points: T =Σ 1 / 2 m k υ 2 k . Expression K. e. systems can also be represented in the form T = 1 / 2 Mυ s 2 + Tc, Where M- mass of the entire system, υ c- speed of the center of mass, Tc - K. e. system in its motion around the center of mass. K. e. solid, moving translationally, is calculated in the same way as K. e. a point having a mass equal to the mass of the entire body. Formulas for calculating K. e. of a body rotating around a fixed axis, see Art. Rotational movement.
Change in K. e. system when it is moved from its position (configuration) 1
to position 2
occurs under the influence of external and internal forces applied to the system and is equal to the sum of work 
.
This equality expresses the theorem on the change of the dynamic energy, with the help of which many problems of dynamics are solved.
At speeds close to the speed of light, K. e. material point
Where m 0- mass of a point at rest, With- speed of light in vacuum ( m 0 s 2- energy of a point at rest). At low speeds ( υ<< c ) the last relation goes into the usual formula 1 / 2 mυ 2.
Kinetic energy.
Kinetic energy - energy of a moving body. (From the Greek word kinema - movement). By definition, the kinetic energy of a body at rest in a given frame of reference vanishes.
Let the body move under the influence constant force in the direction of the force.
Then: 
.
Because motion is uniformly accelerated, then: .
Hence: 
.
- kinetic energy is called
Dynamic anatomy
ANALYSIS OF POSITIONS AND MOVEMENTS OF THE HUMAN BODY.
The main provisions of this theoretical course were developed by P.F. Lesgaft and was called “Course on the Theory of Bodily Movements”. This course included an analysis of the general laws of human structure, movement in joints, and the position of the human body in space during movement.
Analysis of body positions in space involved the study of human movements in a certain sequence:
- Morphology of movement or position– was based on a purely visual familiarization with the pose, the exercise that was supposed to be performed. At the same time, the position in space of the body and its individual parts - the head, torso, and limbs - was examined in detail.
- Mechanics of body positions– at the same time, the exercise proposed for implementation was considered from the point of view of the laws of mechanics. And this presupposed mandatory familiarization with the forces that have an effect on the human body.
Any movement, exercise, or position of the body is carried out through the interaction of forces that act on the human body. These forces are divided into external and internal.
EXTERNAL FORCES– forces acting on a person from the outside, during his interaction with external bodies (earth, gymnastic equipment, any objects).
1. GRAVITY is the force with which a body is attracted to the ground. It is equal to the weight or mass of the body, applied to its center and directed vertically downward. The point of application of this force is the general center of gravity of the body - GCT. GCT consists of the centers of gravity of individual body segments.
When the body moves downward gravity is the driving force, those. helps movement;
When driving up– slows down movement (interferes);
When driving along horizontal– has a neutral effect.
2. GROUP REACTION FORCE is the force with which the support area acts on the body.
Moreover, if the body retains vertical position, then the support reaction force is equal to the force of gravity and directed opposite to it, i.e. . up.
When walking, running, or standing long jumps, the reaction force of the support will be directed at an angle to the area of support and, according to the rule of parallelogram of forces, can be decomposed into vertical and horizontal components.
A. VERTICAL COMPONENT OF THE SUPPORT REACTION FORCE– directed upward, opposite to gravity (its mirror image).
B. HORIZONTAL COMPONENT (RESISTS FRICTION FORCE)– directed opposite to the direction of movement. Without friction, movement is impossible. Sometimes this strength is artificially increased - tartan coverings on treadmills.
3. POWER OF RESISTANCE TO THE EXTERNAL ENVIRONMENT- this force can either inhibit movement or promote it.
The braking influence of the environment can be reduced by adopting the most favorable (streamlined) body shape, and the drag force of the environment can be increased by increasing the repulsion surface (for swimmers - fins, for rowers - an oar blade).
4. FORCE OF INERTIA – force that occurs when a body moves with acceleration. Rational use of inertial force allows you to save muscle energy. This power may be centripetal, i.e. directed towards the center of rotation and centrifugal– directed from the center of rotation. These forces are opposite in direction. If they are equal, then the body remains at rest; if not, then the body moves towards the larger of them. For a runner, the force of the tailwind is the driving force, i.e. helps the movement, and the force of the headwind acts as a brake.
A mechanical system is a set of material points united by the conditions of the problem.
(If the distances between points of the system do not change, then such a system is called a rigid body.)
Forces acting on points of a mechanical system:
External forces are those acting on points of a system from points or bodies that are not part of the system.
Internal forces are those with which points or bodies of a given system act on each other.
Properties of internal forces:
· The geometric sum (principal vector) of all internal forces of the system is equal to zero.
According to the third law of dynamics, any two points of the system act on each other with forces equal in magnitude and oppositely directed, the sum of which is zero. Since a similar result holds for any pair of points in the system, then
· The sum of moments (principal moment) of all internal forces of the system relative to any center or axis is equal to zero.
From these properties it follows that the internal forces are mutually balanced and do not affect the movement of the system, because these forces are applied to different material points or bodies and can cause mutual movements of these points or bodies. The entire set of internal forces will be balanced in a system that is an absolutely solid body.
Ticket number 19.
Center of mass of a mechanical system. Theorem on the motion of the center of mass of a mechanical system. Corollary of the theorem.
The center of mass (C) is a point whose position is determined by the equation:
By projecting equation (2)!!! on OX, OY, OZ we get:
ADDITIONALLY(!)
Theorem on the motion of the center of mass:
Let there be a mechanical system consisting of n points. For each point, we will write the basic equation of dynamics, taking into account the fact that both external and internal forces can act on the point:
Formulation:
The product of the mass of a system and the acceleration of its center of mass is equal to the geometric sum of all external forces acting on the system.
Projecting (5a) on the OX, OY, OZ axes we obtain:
Corollary of the theorem:
If the sum of external forces (projection of external forces onto any axis) is equal to zero, then the acceleration of the center of mass (projection onto the corresponding axis) is equal to zero. This means that the speed of the center of mass (velocity projection) is constant. And if this speed was equal to zero, then the position of the center of mass (the corresponding coordinate) does not change.
Ticket number 20.
The amount of motion of a mechanical system. Theorem on the change in momentum of a mechanical system.
The quantity of motion of the system will be called the vector quantity Q, equal to the geometric sum (principal vector) of the quantities of motion of all points of the system:
Those. The momentum of the system is equal to the product of the mass of the entire system and the speed of its center of mass.
Theorem on the change in momentum of a mechanical system:
Let there be a mechanical system consisting of n points. For each, we write equation (7a), taking into account the fact that both external and internal forces act on the point.
Statement of the theorem:
The time derivative of the system's momentum is equal to the geometric sum of all external forces acting on the system.
The theorem on the change in momentum of a mechanical system in differential form:
Multiplying both sides of equation (7c) by dt we get:
The change in the momentum of a mechanical system over a certain period t is equal to the sum of the impulses applied to a point in the mechanical system over the same period of time.
How can you find the number of movements of the system?
