Conditions for equilibrium of a body that has an axis. Three types of equilibrium of bodies that have a fulcrum

Definition

The equilibrium of a body is a state when any acceleration of the body is equal to zero, that is, all the actions of forces and moments of forces on the body are balanced. In this case, the body can:

be in a state of calm;
move evenly and straightly;
rotate uniformly around an axis that passes through its center of gravity.

Body equilibrium conditions

If the body is in equilibrium, then two conditions are simultaneously satisfied.

The vector sum of all forces acting on the body is equal to the zero vector: $\sum_n((\overrightarrow(F))_n)=\overrightarrow(0)$
The algebraic sum of all moments of forces acting on the body is equal to zero: $\sum_n(M_n)=0$

Two equilibrium conditions are necessary but not sufficient. Let's give an example. Consider a wheel rolling uniformly without slipping along horizontal surface. Both equilibrium conditions are satisfied, but the body moves.

Let's consider the case when the body does not rotate. In order for the body not to rotate and to be in equilibrium, it is necessary that the sum of the projections of all forces on an arbitrary axis equals zero, that is, the resultant of the forces. Then the body is either at rest or moving evenly and in a straight line.

A body that has an axis of rotation will be in equilibrium state, if the rule of moments of forces is satisfied: the sum of the moments of forces that rotate the body clockwise must be equal to the sum of the moments of forces that rotate it counterclockwise.

To get right moment at with the least effort, you need to apply force as far as possible from the axis of rotation, thereby increasing the leverage of the force and correspondingly decreasing the value of the force. Examples of bodies that have an axis of rotation are: lever, doors, blocks, rotation axis, etc.

Three types of equilibrium of bodies that have a fulcrum

stable equilibrium, if the body, being removed from the equilibrium position to the next closest position and left at rest, returns to this position;
unstable equilibrium, if the body, being taken from a position of equilibrium to an adjacent position and left at rest, will deviate even more from this position;
indifferent equilibrium - if the body, being brought to an adjacent position and left calm, remains in its new position.

Equilibrium of a body with a fixed axis of rotation

stable if in the equilibrium position the center of gravity C occupies the lowest position of all possible nearby positions, and its potential energy will have smallest value of all possible values in adjacent positions;
unstable if the center of gravity C occupies the highest of all nearby positions, and the potential energy has the greatest value;
indifferent if the center of gravity of the body C in all nearby possible positions is at the same level, and the potential energy does not change during the transition of the body.

Problem 1

Body A with mass m = 8 kg is placed on a rough horizontal table surface. A thread is tied to the body, thrown over block B (Figure 1, a). What weight F can be tied to the end of the thread hanging from the block so as not to upset the balance of body A? Friction coefficient f = 0.4; Neglect friction on the block.

Let us determine the weight of the body ~A: ~G = mg = 8$\cdot $9.81 = 78.5 N.

We assume that all forces are applied to body A. When the body is placed on a horizontal surface, only two forces act on it: weight G and the oppositely directed reaction of the support RA (Fig. 1, b).

If we apply some force F acting along a horizontal surface, then the reaction RA, balancing the forces G and F, will begin to deviate from the vertical, but body A will be in equilibrium until the modulus of force F exceeds maximum value friction force Rf max corresponding to the limiting value of the angle $(\mathbf \varphi )$o (Fig. 1, c).

By decomposing the reaction RA into two components Rf max and Rn, we obtain a system of four forces applied to one point (Fig. 1, d). By projecting this system of forces onto the x and y axes, we obtain two equilibrium equations:

$(\mathbf \Sigma )Fkx = 0, F - Rf max = 0$;

$(\mathbf \Sigma )Fky = 0, Rn - G = 0$.

We solve the resulting system of equations: F = Rf max, but Rf max = f$\cdot $ Rn, and Rn = G, so F = f$\cdot $ G = 0.4$\cdot $ 78.5 = 31.4 N; m = F/g = 31.4/9.81 = 3.2 kg.

Answer: Cargo mass t = 3.2 kg

Problem 2

The system of bodies shown in Fig. 2 is in a state of equilibrium. Cargo weight tg=6 kg. The angle between the vectors is $\widehat((\overrightarrow(F))_1(\overrightarrow(F))_2)=60()^\circ $. $\left|(\overrightarrow(F))_1\right|=\left|(\overrightarrow(F))_2\right|=F$. Find the mass of the weights.

The resultant forces $(\overrightarrow(F))_1and\ (\overrightarrow(F))_2$ are equal in magnitude to the weight of the load and opposite to it in direction: $\overrightarrow(R)=(\overrightarrow(F))_1+(\overrightarrow (F))_2=\ -m\overrightarrow(g)$. By the cosine theorem, $(\left|\overrightarrow(R)\right|)^2=(\left|(\overrightarrow(F))_1\right|)^2+(\left|(\overrightarrow(F) )_2\right|)^2+2\left|(\overrightarrow(F))_1\right|\left|(\overrightarrow(F))_2\right|(cos \widehat((\overrightarrow(F)) _1(\overrightarrow(F))_2)\ )$.

Hence $(\left(mg\right))^2=$; $F=\frac(mg)(\sqrt(2\left(1+(cos 60()^\circ \ )\right)))$;

Since the blocks are movable, then $m_g=\frac(2F)(g)=\frac(2m)(\sqrt(2\left(1+\frac(1)(2)\right)))=\frac(2 \cdot 6)(\sqrt(3))=6.93\ kg\ $

Answer: the mass of each weight is 6.93 kg

A body is at rest (or moves uniformly and rectilinearly) if the vector sum of all forces acting on it is equal to zero. They say that forces balance each other. When we are dealing with a certain body geometric shape, when calculating the resultant force, all forces can be applied to the center of mass of the body.

Condition for equilibrium of bodies

For a body that does not rotate to be in equilibrium, it is necessary that the resultant of all forces acting on it be equal to zero.

F → = F 1 → + F 2 → + . . + F n → = 0 .

The figure above shows the equilibrium of a rigid body. The block is in a state of equilibrium under the influence of three forces acting on it. The lines of action of the forces F 1 → and F 2 → intersect at point O. The point of application of gravity is the center of mass of the body C. These points lie on the same straight line, and when calculating the resultant force F 1 →, F 2 → and m g → are brought to point C.

The condition that the resultant of all forces be equal to zero is not enough if the body can rotate around a certain axis.

The arm of force d is the length of the perpendicular drawn from the line of action of the force to the point of its application. The moment of force M is the product of the force arm and its modulus.

The moment of force tends to rotate the body around its axis. Those moments that turn the body counterclockwise are considered positive. Unit of measurement of moment of force in international system SI - 1 Newton meter.

Definition. Rule of Moments

If algebraic sum of all moments applied to the body relative to the fixed axis of rotation is equal to zero, then the body is in a state of equilibrium.

M 1 + M 2 + . . +Mn=0

Important!

IN general case For bodies to be in equilibrium, two conditions must be met: the resultant force must be equal to zero and the rule of moments must be observed.

In mechanics there is different types balance. Thus, a distinction is made between stable and unstable, as well as indifferent equilibrium.

A typical example of indifferent equilibrium is a rolling wheel (or ball), which, if stopped at any point, will be in a state of equilibrium.

Stable balance- such an equilibrium of a body when, with its small deviations, forces or moments of force arise that tend to return the body to an equilibrium state.

Unstable equilibrium- a state of equilibrium, with a small deviation from which forces and moments of forces tend to throw the body out of balance even more.

In the figure above, the position of the ball is (1) - indifferent equilibrium, (2) - unstable equilibrium, (3) - stable equilibrium.

Body with fixed axis rotation can be in any of the described equilibrium positions. If the axis of rotation passes through the center of mass, indifference equilibrium occurs. In stable and unstable equilibrium, the center of mass is located on a vertical straight line that passes through the axis of rotation. When the center of mass is below the axis of rotation, the equilibrium is stable. Otherwise, it's the other way around.

A special case of balance is the balance of a body on a support. At the same time elastic force distributed throughout the base of the body, rather than passing through one point. A body is at rest in equilibrium when vertical line, drawn through the center of mass, intersects the area of support. Otherwise, if the line from the center of mass does not fall into the contour, formed by lines connecting the support points, the body tips over.

An example of body balance on a support is the famous Leaning Tower of Pisa. According to legend, Galileo Galilei dropped balls from it when he conducted his experiments on studying free fall tel.

A line drawn from the center of mass of the tower intersects the base approximately 2.3 m from its center.

If you notice an error in the text, please highlight it and press Ctrl+Enter

1. What is studied in statics.

2. Equilibrium of bodies in the absence of rotation.

3. Equilibrium of bodies with a fixed axis of rotation. Moment of power. Rule of moments. Leverage rule.

4. Types of equilibrium of bodies (stable and unstable). Center of gravity.

1. We already know that Newton’s laws allow us to find out what accelerations bodies receive under the influence of forces applied to them. But very often it is important to know under what conditions the bodies on which they can act various forces, do not receive accelerations. Such bodies are said to be in a state of equilibrium. In particular, bodies at rest are in this state. Knowing the conditions under which bodies are at rest is very important for practice, for example, in the construction of buildings, bridges, all kinds of supports, suspensions, in the manufacture of machines, instruments, etc. This question is also no less important for you! But the basics of balance in sports are dealt with in more detail by a science such as biomechanics, which you will study in your third year.

Mechanics deals with more general issues. That part of mechanics in which the equilibrium of solid bodies is studied is called static. It is known that any body can move translationally and, in addition, rotate or rotate around some axis. For a body to be at rest, it must neither move translationally nor rotate or rotate around any axis. Let us consider the conditions of equilibrium of bodies for these two types of possible motion separately. And Newton’s laws will help us find out exactly what conditions ensure the equilibrium of bodies.

2. Equilibrium of bodies in the absence of rotation. During the translational motion of a body, we can consider the movement of only one point of the body - its center of mass. In this case, we must assume that the entire mass of the body is concentrated at the center of mass and the resultant of all forces acting on the body is applied to it. (The force that alone can impart to a body the same acceleration as all the forces simultaneously acting on it, taken together, is called the resultant of these forces).

From Newton's second law it follows that the acceleration of this point is equal to zero if the geometric sum of all forces applied to it - the resultant of these forces - is equal to zero. This is the condition for the equilibrium of a body in the absence of its rotation.

In order for a body that can move translationally (without rotation) to be in equilibrium, it is necessary that the geometric sum of the forces applied to the body be equal to zero. But if the geometric sum of forces is zero, then the sum of the projections of the vectors of these forces onto any axis is also zero. Therefore, the condition for the equilibrium of a body can be formulated as follows: for a non-rotating body to be in equilibrium, it is necessary that the sum of the forces applied to the body on any axis be equal to zero.

For example, a body is in equilibrium to which two equal forces are applied, acting along one straight line, but directed in opposite directions (Fig. 1).

A state of balance is not necessarily a state of rest. From Newton's second law it follows that when the resultant of the forces applied to a body is zero, the body can move rectilinearly and uniformly. With this movement, the body is also in a state of balance.

For example, a skydiver, after he begins to fall at a constant speed, is in a state of equilibrium. In Figure 1, the forces are applied to the body at more than one point. But what is important is not the point of application of the force, but the straight line along which it acts. Shifting the point of application of force along the line of its action does not change anything either in the movement of the body or in the state of equilibrium. It is clear, for example, that nothing will change if, instead of pulling the trolley, they start pushing it. If the resultant of the forces applied to the body is not zero, then in order for the body to be in a state of equilibrium, an additional force must be applied to it, equal in magnitude to the resultant, but opposite to it in direction.

This force is called balancing.

3. Equilibrium of bodies with a fixed axis of rotation. Moment of power.Rule of moments. Leverage rule. A couple of forces.

So, the conditions for equilibrium of a body in the absence of rotation have been clarified. But how is the absence of body rotation ensured? To answer this question, consider a body that cannot perform translational motion, but can turn or rotate. To make the forward movement of a body impossible, it is enough to fix it at one point in the same way as you can, for example, fix a board on a wall by nailing it with one nail; the forward movement of such a board becomes impossible, but the board can rotate around the nail, which serves as its axis of rotation.

Now let's find out which forces cannot and which can cause rotation (rotation) of a body with a fixed axis of rotation. Let's consider some body (see Fig. 2) that can rotate around an axis perpendicular to the plane of the drawing. From this figure it can be seen that the forces F 1 ,F 2 and F 3 will not cause the body to rotate. Lines them

actions pass through the axis of rotation. Any such force will be balanced by the reaction force of the fixed axle. Rotation (or rotation) can only be caused by forces, lines, whose actions do not pass through the axis of rotation. Strength F 1 , for example, applied to a body as shown in Figure 3, will cause the body to rotate clockwise, the force F 2 will cause the body to rotate counterclockwise.

To make a turn or rotation impossible, it is obvious that at least two forces must be applied to the body: one causing a clockwise turn, the other counter-clockwise. But these two forces may not be equal to each other (in absolute value). For example, strength F 2 (see Fig. 4) causes the body to rotate counterclockwise.

Experience shows that it can be balanced by force F 1 , causing the body to rotate clockwise, but in magnitude less than the forceF 2. This means that these two forces, unequal in magnitude, have the same, so to speak, “rotating action.” What do they have in common, what is the same for them? Experience shows

that in this case the product of the modulus of force and the distance from the axis of rotation to the line of action of the force is the same (the word “distance” here means the length of the perpendicular lowered from the center of rotation to the direction of action of the force). This is the distance calledshoulder of strength. Force arm F 1 - this is d 1 , shoulder strengthf 2 - this is d 2 .  F 1  d 1 = F 2 d 2 ;

M = | f| d So, the “rotational action” of a force is characterized by the product of the force modulus and its shoulder. A value equal to the product of the modulus of force F on her shoulder d, called moment of force relative to the axis of rotation. The words “relative to the axis” in the definition of moment are necessary because if, without changing either the modulus of the force or its direction, the axis of rotation is moved from point O to another point, then the arm of the force, and therefore the moment of force, will change. The moment of force characterizes the rotational action of this force and plays the same role in rotational motion as the force in translational motion.

The moment of force depends on two quantities: on the modulus of the force itself and on its shoulder. The same moment of force can be created by a small force whose leverage is large and by a large force with a small leverage. If, for example, you try to close a door by pushing it close to the hinges, then this can be successfully counteracted by a child who will think of pushing it in the other direction, applying force closer to the edge, and the door will remain alone. For a new quantity - moment of force - you need to find a unit. The unit of moment of force in SI is taken to be a moment of force in 1N, the line of action of which is 1 m away from the axis of rotation. This unit is called the newton meter (N m).

Moments of forces rotating a body clockwise are usually assigned a positive sign, and those rotating a body counterclockwise are assigned a negative sign.

Then moments of strength F 1 and F 2 relative to the O axis have opposite signs and their algebraic sum is zero. Thus, we can write the equilibrium condition for a body with a fixed axis: F 1 d 1 =F 2 d 2 or – F 1 d 1 +F 2 d 2 =0, M 1 +M 2 =0.

Consequently, a body with a fixed axis of rotation is in equilibrium if the algebraic sum of the moments of all forces acting on the body relative to a given axis is equal to zero, i.e. if the sum of the moments of forces acting on a body clockwise is equal to the sum of the moments of forces acting on the body counterclockwise.

This condition of equilibrium of bodies with a fixed axis of rotation is called rule of moments.

Levers. Leverage rule

It is easy to understand that the famous rule of leverage follows from the rule of moments.

Lever is a rigid body that has a fixed axis of rotation and is acted upon by forces tending to rotate it around this axis. There are levers of the first and second years. A lever of the first kind is a lever whose axis of rotation is located between the points of application of forces, and the forces themselves are directed in the same direction (see Fig. 5). Examples of levers of the first kind are the yoke of equal-armed scales, a railway barrier, a well crane, scissors, etc.

A lever of the second kind is a lever whose axis of rotation is located on one side of the points of application of forces, and the forces themselves are directed opposite to each other (see Fig. 6). Examples of levers of the second kind are wrenches, various pedals, nutcrackers, doors etc. According to the rule of moments, a lever (of any kind) is balanced only when M 1 = M 2. Since M 1 =F 1 d 1 and M 2 =F 2 d 2, we obtain F 1 d 1 =F 2 d 2. From the last

the formula follows that F 1 /F 2 =d 1 /d 2. A lever is in equilibrium when the forces acting on it are inversely proportional to their arms. But this is nothing more than another expression of the moment rule: F 1 / F 2 = d 1 / d 2 . From the last formula it is clear that with the help of a lever, the greater the leverage ratio, the greater the strength gain. This is widely used in practice.

A couple of forces. Two antiparallel forces of equal magnitude applied to a body in different points, is called a couple of forces. Examples of a pair of forces are the forces that are applied to the steering wheel of a car, electrical forces, magnetic forces acting on the dipole, acting on the magnetic needle, etc. (see Figure 7).

A pair of forces does not have a resultant, i.e. joint action these forces cannot be replaced by the action of one force. Therefore, a pair of forces cannot cause translational motion of the body, but only causes it to rotate. If, when a body rotates under the action of a pair of forces, the directions of these forces do not change, then the body rotates until both forces act opposite to each other along a straight line passing through the axis of rotation of the body.

Let a body with a fixed axis of rotation O be acted upon by a pair of forces f And f(see Fig. 8). The moments of these forces M 1 =| f|d 1<0 и M 2 =|f| d 2<0. Сумма моментов M 1 +M 2 =|f|(d 1 +d 2)= =|f|d0, следовательно, тело не находится в равновесии. Кратчайшее расстояние d=d 1 +d 2 между параллельными прямыми,

along which the forces acting, forming a pair of forces, are called the arm of the pair of forces; M=|f|d is the moment of a couple of forces. Consequently, the moment of a pair of forces is equal to the product of the modulus of one of the forces of this pair and the shoulder of the pair, regardless of the position of the axis of rotation of the body, provided that this axis is perpendicular to the plane in which the pair of forces is located.

If a pair of forces acts on a body that does not have a fixed axis of rotation, it causes rotation of this body around an axis extending through the center of mass of this body.

4. Types of body balance.

If a body is in equilibrium, this means that the sum of the forces applied to it is zero and the sum of the moments of these forces relative to the axis of rotation is also zero. But the question arises: is the equilibrium stable? ( F= 0,M= 0).

At first glance, it is clear, for example, that the equilibrium position of a ball on the top of a convex stand is unstable: the slightest deviation of the ball from its equilibrium position will lead to it rolling down. Let's place the same ball on a concave stand. It is not so easy to make him leave his place. The equilibrium of the ball can be considered stable.

What is the secret of sustainability? In the cases we have considered, the ball is in equilibrium: gravity f t, equal in magnitude to the oppositely directed elastic force (reaction force) N from the support side. The whole point, it turns out, is precisely that slightest deviation that we mentioned. Figure 9 shows that as soon as the ball on the convex stand left its place, the force of gravity f t ceases to be balanced by force N from the support side (force N always directed

perpendicular to the contact surface of the ball and the stand). Resultant of gravity f t and support reaction force N, i.e. force F is directed so that the ball moves even further away from its equilibrium position. The situation is different on the concave stand (Fig. 10). With a small deviation from the initial position, the balance is also disturbed here. The elastic force on the side of the support will no longer balance the force of gravity. But now the resultant of these forces F T is directed so that the body returns to its previous position. This is the condition for the stability of equilibrium.

The balance of the body is stable, if, with a small deviation of the equilibrium position, the resultant of the forces applied to the body returns it to the equilibrium position.

The balance is unstable if, with a small deviation of the body from the equilibrium position, the resultant of the forces applied to the body removes it from this position.

This is also true for a body that has an axis of rotation. As an example of such a body, consider an ordinary ruler mounted on a rod passing through a hole near its end. From Figure 11a it is clear that the position of the ruler is stable. If you hang the same ruler as shown in another figure 11b, then the equilibrium of the ruler will be unstable.

Stable and unstable equilibrium positions are also separated from each other by the position of the body’s center of gravity.

The center of gravity of a solid body is the point of application of the resultant of all gravity forces acting on each particle of this body. The center of gravity of a solid body coincides with its center of mass. Therefore, the center of mass is often called the center of gravity. However, there is a difference between these concepts. The concept of the center of gravity is valid only for a solid body located in a uniform field of gravity, and the concept of the center of mass is not associated with any force field and is valid for any body (mechanical system).

So, for stable balance, the center of gravity of the body must be in the lowest possible position for it.

The equilibrium of a body with an axis of rotation is stable provided that its center of gravity is located below the axis of rotation.

It is also possible to have an equilibrium position where deviations from it do not lead to any changes in the state of the body. This is, for example, the position of a ball on a flat support or a ruler suspended on a rod passing through its center of gravity. This equilibrium is called indifferent.

We examined the condition of equilibrium of bodies that have a fulcrum or an axis of support. No less important is the case when the support is not on a point (axis), but on some surface.

A body having a support area is in equilibrium; when a vertical line passing through the center of gravity of a body does not extend beyond the area of support of this body. The same cases of body equilibrium are distinguished as mentioned above. However, the equilibrium of a body with a support area depends not only on the distance of its center of gravity from the Earth, but also on the location and size of the support area of this body. In order to be able to simultaneously take into account both the height of the center of gravity of a body above the Earth and the value of its support area, the concept of the angle of stability of the body was introduced.

The angle of stability is the angle formed by the horizontal plane and the straight line connecting the center of gravity of the body with the edge of the support area. As can be seen from Figure 12, the angle of stability decreases if the center of gravity of the body is lowered in some way (for example, the lower part of the body is made more massive or part of the body is buried in the Earth, i.e., they create a foundation, and also increase the area of support for the body). The smaller the angle of stability, the more stable the balance of the body.

Conclusion: in order for any body to be in equilibrium, two conditions must be simultaneously met: firstly, the vector sum of all forces applied to the body must be equal to zero and, secondly, the algebraic sum of the moments of all forces acting on the body must be equal to zero forces relative to an arbitrary fixed axis.

Start typing part of the condition (for example, can , what is equal to or find ):

17. Equilibrium of bodies in the absence of rotation

No. 325. Find the resultant of three forces of 100 N each if the angle between the first and second forces is 60°, and between the second and third is 90°.
No. 326. With which method of hanging the swing (Fig. 60) will the ropes experience less tension?
β, therefore, cosβ > cosα and T1 > T2. "> No. 327. Why does a tightly stretched clothesline often break under the weight of a dress hung on it, while a loosely stretched one can withstand the same load?
No. 328. Are the readings of both dynamometers the same (Fig. 61), is the block axis experiencing the same pressure force in both cases?
No. 329. The system of movable and fixed blocks is in equilibrium (Fig. 62). What happens if point A of the thread attachment is moved to the right?
No. 330. A body of mass 2 kg is suspended by a thread. Another thread was tied to the body and pulled horizontally. Find the tension force on the string at the new equilibrium position if the tension force on the horizontal string is 12 N.
No. 331. You can move a body uniformly and rectilinearly along a horizontal surface by applying forces to it, as shown in Figure 63. Are these forces the same if the coefficient of friction is the same in both cases?
No. 332. There is only one suit hanging on a clothesline 10 m long, weighing 20 N. The hanger is located in the middle of the rope, and this point sags 10 cm below the horizontal line drawn through the points of attachment of the rope. What is the tension in the rope?
No. 333. Find the forces acting on rods AB and BC (Fig. 64) if α = 60° and the mass of the lamp is 3 kg.
No. 334. A load weighing 120 kg is suspended from the end of a rod AC (Fig. 65) 2 m long, hinged at one end to the wall, and at the other end supported by a cable BC 2.5 m long. Find the forces acting on the cable and the rod.
No. 335. An electric lamp (Fig. 66) is suspended on a cord and pulled back by a horizontal guy. Find the tension force of the cord and guy wire if the mass of the lamp is 1 kg and the angle α = 60°.
No. 336. A heavy homogeneous ball is suspended on a thread, the end of which is fixed to a vertical wall. The point of attachment of the ball to the thread is on the same vertical as the center of the ball. What should be the coefficient of friction between the ball and the wall so that the ball is in equal
No. 337. A ball of radius r and mass m is held on a stationary ball of radius R by a weightless inextensible thread of length l, fixed at the top point C of the ball (Fig. 67). There are no other points of contact between the ball and the thread. Find the tension in the thread. Friction

Let the body be fixed on a fixed axis (section 1.4) and a force applied to it in one of two ways:

1) the line of action passes through the axis of rotation. will be balanced by the reaction and the body will be in balance;

2) the line of action does not pass through the axis of rotation, which leads to rotation of the body.

Let us apply a force to the body causing it to rotate in the opposite side. Under certain conditions, rotation may become uniform or stop altogether. It is known from experiments that this will happen if , where d 1 and d 2 – shoulders strength and .

Shoulder of power(d)relative to the axis – shortest distance from the line of action of the force to this axis.

moment of force (M) is the product of the force modulus and its shoulder.

[M] = 1 Nm

· In this paragraph, the moment is considered as scalar quantity, and the forces and their shoulders lie in a plane perpendicular to the axis of rotation.

· The moment of force rotating a body clockwise is considered negative, counter-clockwise is considered positive.

The equilibrium condition is known as rule of moments: a body with a fixed axis of rotation is in equilibrium if the algebraic sum of the moments of all forces applied to it is equal to zero.

Full condition equilibrium (for any bodies)

A body is in equilibrium if the resultant of all forces applied to it is zero and the sum of the moments of these forces relative to the axis of rotation is also zero.

Types of balance

1. Stable balance- equilibrium, upon exiting which a force arises that returns the body to its original position.

2. Unstable equilibrium- equilibrium, upon exiting which a force arises, further deflecting the body from its original position.

3. Indifferent Equilibrium - equilibrium, upon exiting which neither a restoring nor a deflecting force arises.

MOLECULAR PHYSICS

Molecular physics– a branch of physics in which the phenomena of changes in the state of bodies and substances are explained from the point of view internal structure substances.

Origins molecular physics

Representations of the Ancients

Ancient philosophical schools explained the structure of bodies and substances in different ways. For example, in China, scientists believed that bodies consist of water, fire, ether, air, etc. Leucippus (5th century BC, Greece) and Democritus (5th century BC, Greece) expressed the idea that:

1) all bodies consist of tiny particles– atoms;

2) differences between bodies are determined either by the difference in their atoms, or by the difference in the arrangement of atoms.

Development of molecular physics

Mikhail Vasilyevich Lomonosov (1711–1765, Russia) made a great contribution to science. He developed the idea of the molecular (atomic) structure of matter and suggested that:

1) particles (molecules) move chaotically;

2) the speed of movement of molecules is related to the temperature of the substance (the higher the temperature, the higher the speed);

3) there must be a temperature at which the movement of molecules stops.

Experiments conducted in the 19th century confirmed the correctness of his ideas.

Brown's experience

In 1827, botanist Robert Brown (1773–1858, England) placed a liquid with small solid particles in it under a microscope and found that:

1) particles move chaotically;

2) than smaller particle, the more noticeable its movement;

He came to the conclusion that shocks to solid particles are given by liquid particles during collisions. The work of many scientists developed the doctrine of the structure and properties of matter - molecular kinetic theory (MKT), based on the idea of the existence of molecules (atoms).

Basic provisions of the ICT

1) Substances consist of particles: atoms and molecules;

2) particles move chaotically;

3) particles interact with each other.

Based on these provisions, the following phenomena were explained: the elasticity of gases, liquids and solids; transfer of matter from one state of aggregation to another; expansion of gases; diffusion etc.

Physical state(thermodynamic phase)– one of three states substances (solid, liquid, gaseous).

Diffusion– spontaneous mixing of substances.