If a body is brought into rotation by a force, then its energy increases by the amount of work expended. As in translational motion, this work depends on the force and the displacement produced. However, the displacement is now angular and the expression for working when moving a material point is not applicable. Because the body is absolutely rigid, then the work of the force, although it is applied at a point, is equal to the work expended on turning the whole body.
When turning through an angle, the point of application of the force travels a path. In this case, the work is equal to the product of the projection of the force on the direction of displacement by the magnitude of the displacement: ; From fig. it can be seen that is the arm of the force, and is the moment of the force.
Then elementary work: . If , then .
The work of rotation goes to increase the kinetic energy of the body
; Substituting , we get: or taking into account the equation of dynamics: , it is clear that , i.e. the same expression.
6. Non-inertial frames of reference
End of work -
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All topics in this section:
mechanical movement
Matter, as is known, exists in two forms: in the form of substance and field. The first type includes atoms and molecules, from which all bodies are built. The second type includes all types of fields: gravity
Space and time
All bodies exist and move in space and time. These concepts are fundamental to all natural sciences. Any body has dimensions, i.e. its spatial extent
Reference system
To unambiguously determine the position of a body at an arbitrary point in time, it is necessary to choose a reference system - a coordinate system equipped with a clock and rigidly connected to an absolutely rigid body, according to
Kinematic equations of motion
When t.M moves, its coordinates and change with time, therefore, to set the law of motion, it is necessary to specify the type of
Movement, elementary movement
Let point M move from A to B along a curved path AB. At the initial moment, its radius vector is equal to
Acceleration. Normal and tangential accelerations
The movement of a point is also characterized by acceleration - the speed of change in speed. If the speed of a point in an arbitrary time
translational movement
The simplest form of mechanical motion of a rigid body is translational motion, in which the straight line connecting any two points of the body moves with the body, remaining parallel | its
Law of inertia
Classical mechanics is based on Newton's three laws, formulated by him in the work "Mathematical Principles of Natural Philosophy", published in 1687. These laws were the result of a genius
Inertial frame of reference
It is known that mechanical motion is relative and its nature depends on the choice of reference frame. Newton's first law is not valid in all frames of reference. For example, bodies lying on a smooth surface
Weight. Newton's second law
The main task of dynamics is to determine the characteristics of the motion of bodies under the action of forces applied to them. It is known from experience that under the influence of force
The basic law of the dynamics of a material point
The equation describes the change in the motion of a body of finite dimensions under the action of a force in the absence of deformation and if it
Newton's third law
Observations and experiments show that the mechanical action of one body on another is always an interaction. If body 2 acts on body 1, then body 1 necessarily counteracts those
Galilean transformations
They allow one to determine the kinematic quantities in the transition from one inertial frame of reference to another. Let's take
Galileo's principle of relativity
The acceleration of any point in all frames of reference moving relative to each other in a straight line and uniformly is the same:
Conserved quantities
Any body or system of bodies is a collection of material points or particles. The state of such a system at some point in time in mechanics is determined by setting the coordinates and velocities in
Center of mass
In any system of particles, you can find a point called the center of mass
Equation of motion of the center of mass
The basic law of dynamics can be written in a different form, knowing the concept of the center of mass of the system:
Conservative forces
If a force acts on a particle placed there at each point in space, it is said that the particle is in a field of forces, for example, in the field of gravity, gravitational, Coulomb and other forces. Field
Central Forces
Any force field is caused by the action of a certain body or system of bodies. The force acting on a particle in this field is about
Potential energy of a particle in a force field
The fact that the work of a conservative force (for a stationary field) depends only on the initial and final positions of the particle in the field allows us to introduce the important physical concept of potentially
Relationship between potential energy and force for a conservative field
The interaction of a particle with surrounding bodies can be described in two ways: using the concept of force or using the concept of potential energy. The first method is more general, because it applies to forces
Kinetic energy of a particle in a force field
Let a particle with mass move in forces
Total mechanical energy of a particle
It is known that the increment in the kinetic energy of a particle when moving in a force field is equal to the elementary work of all forces acting on the particle:
Law of conservation of mechanical energy of a particle
It follows from the expression that in a stationary field of conservative forces, the total mechanical energy of a particle can change
Kinematics
Rotate the body through some angle
The angular momentum of the particle. Moment of power
In addition to energy and momentum, there is another physical quantity with which the conservation law is associated - this is the angular momentum. Particle angular momentum
Moment of momentum and moment of force about the axis
Let us take in the frame of reference we are interested in an arbitrary fixed axis
The law of conservation of momentum of the system
Let us consider a system consisting of two interacting particles, which are also acted upon by external forces and
Thus, the angular momentum of a closed system of particles remains constant, does not change with time
This is true for any point in the inertial frame of reference: . Angular moments of individual parts of the system m
Moment of inertia of a rigid body
Consider a rigid body that can
Rigid Body Rotation Dynamics Equation
The equation of the dynamics of rotation of a rigid body can be obtained by writing the equation of moments for a rigid body rotating around an arbitrary axis
Kinetic energy of a rotating body
Consider an absolutely rigid body rotating around a fixed axis passing through it. Let's break it down into particles with small volumes and masses
Centrifugal force of inertia
Consider a disk that rotates with a ball on a spring, put on a spoke, Fig.5.3. The ball is
Coriolis force
When a body moves relative to a rotating CO, in addition, another force appears - the Coriolis force or the Coriolis force
Small fluctuations
Consider a mechanical system whose position can be determined using a single quantity, say x. In this case, the system is said to have one degree of freedom. The value of x can be
Harmonic vibrations
The equation of Newton's 2nd Law in the absence of friction forces for a quasi-elastic force of the form has the form:
Mathematical pendulum
This is a material point suspended on an inextensible thread with a length that oscillates in a vertical plane.
physical pendulum
This is a rigid body that oscillates around a fixed axis associated with the body. The axis is perpendicular to the drawing and
damped vibrations
In a real oscillatory system, there are resistance forces, the action of which leads to a decrease in the potential energy of the system, and the oscillations will be damped. In the simplest case
Self-oscillations
With damped oscillations, the energy of the system gradually decreases and the oscillations stop. In order to make them undamped, it is necessary to replenish the energy of the system from the outside at a certain moment
Forced vibrations
If the oscillatory system, in addition to the resistance forces, is subjected to the action of an external periodic force that changes according to the harmonic law
Resonance
The curve of the dependence of the amplitude of forced oscillations on leads to the fact that for some specific for a given system
Wave propagation in an elastic medium
If a source of oscillations is placed in any place of an elastic medium (solid, liquid, gaseous), then due to the interaction between particles, the oscillation will propagate in the medium from particle to hour
Equation of plane and spherical waves
The wave equation expresses the dependence of the displacement of an oscillating particle on its coordinates,
wave equation
The wave equation is a solution to a differential equation called the wave equation. To establish it, we find the second partial derivatives with respect to time and coordinates from the equation
Here, is the angular momentum relative to the axis of rotation, that is, the projection onto the axis of the angular momentum, defined relative to some point belonging to the axis (see lecture 2). - this is the moment of external forces relative to the axis of rotation, that is, the projection onto the axis of the resulting moment of external forces, defined relative to some point belonging to the axis, and the choice of this point on the axis, as in the case of c, does not matter. Indeed (Fig. 3.4), 
where is the component of the force applied to the rigid body, perpendicular to the axis of rotation, is the shoulder of the force relative to the axis.
 |
| Rice. 3.4. |
Since ( is the moment of inertia of the body relative to the axis of rotation), then instead of we can write
| (3.8) |
The vector is always directed along the axis of rotation, and is the component of the vector of the moment of force along the axis.
In the case, we obtain, respectively, and the angular momentum about the axis is preserved. At the same time, the vector itself L, defined relative to some point on the axis of rotation, may vary. An example of such a movement is shown in Fig. 3.5.
 |
| Rice. 3.5. |
Rod AB, hinged at point A, rotates by inertia around a vertical axis in such a way that the angle between the axis and the rod remains constant. Momentum vector L, relative to point A moves along a conical surface with a half-opening angle, however, the projection L on the vertical axis remains constant, since the moment of gravity about this axis is zero.
Kinetic energy of a rotating body and the work of external forces (the axis of rotation is stationary).
Velocity of the i-th particle of the body
| (3.11) |
where is the distance of the particle to the axis of rotation Kinetic energy
| (3.12) |
as angular velocity rotation for all points is the same.
In accordance with the law of change of mechanical energy system, the elementary work of all external forces is equal to the increment of the kinetic energy of the body:
let us omit that the grindstone disc rotates by inertia with angular velocity and we stop it by pressing some object against the edge of the disc with a constant force. In this case, a force of constant magnitude directed perpendicular to its axis will act on the disk. The work of this force
where is the moment of inertia of the disk sharpened together with the armature of the electric motor.
Comment. If the forces are such that they do not produce work.
free axles. Stability of free rotation.
When a body rotates around a fixed axis, this axis is held in a constant position by bearings. When the unbalanced parts of the mechanisms rotate, the axles (shafts) experience a certain dynamic load, vibrations, shaking occur, and the mechanisms can collapse.
If a rigid body is spun around an arbitrary axis, rigidly connected to the body, and the axis is released from the bearings, then its direction in space, generally speaking, will change. In order for an arbitrary axis of rotation of the body to keep its direction unchanged, certain forces must be applied to it. The resulting situations are shown in Fig. 3.6.
 |
| Rice. 3.6. |
A massive homogeneous rod AB is used here as a rotating body, attached to a sufficiently elastic axis (depicted by double dashed lines). The elasticity of the axle makes it possible to visualize the dynamic loads it experiences. In all cases, the axis of rotation is vertical, rigidly connected to the rod and fixed in bearings; the rod is spun around this axis and left to itself.
In the case shown in Fig. 3.6a, the axis of rotation is the main one for the point B of the rod, but not the central one, the axis bends, from the side of the axis the force that ensures its rotation acts on the rod (in the NISO associated with the rod, this force balances the centrifugal force of inertia). From the side of the rod, a force acts on the axis balanced by the forces from the side of the bearings.
In the case of Fig. 3.6b, the axis of rotation passes through the center of mass of the rod and is central for it, but not the main one. The angular momentum about the center of mass O is not conserved and describes a conical surface. The axis is deformed (breaks) in a complex way, forces act on the rod from the side of the axis and the moment of which provides an increment (In the NISO associated with the rod, the moment of elastic forces compensates for the moment of centrifugal forces of inertia acting on one and the other halves of the rod). From the side of the rod, forces act on the axis and are directed opposite to the forces and The moment of forces and is balanced by the moment of forces and arising in the bearings.
And only in the case when the axis of rotation coincides with the main central axis of inertia of the body (Fig. 3.6c), the rod untwisted and left to itself does not have any effect on the bearings. Such axles are called free axles, because if the bearings are removed, they will keep their direction in space unchanged.
It is another matter whether this rotation will be stable with respect to small perturbations, which always take place in real conditions. Experiments show that rotation around the main central axes with the largest and smallest moments of inertia is stable, and rotation around an axis with an intermediate value of the moment of inertia is unstable. This can be verified by throwing up a body in the form of a parallelepiped, untwisted around one of the three mutually perpendicular main central axes (Fig. 3.7). Axis AA" corresponds to the largest, axis BB" - to the average, and axis CC" - to the smallest moment of inertia of the parallelepiped. quite stable. Attempts to make the body rotate around the axis BB "do not lead to success - the body moves in a complex way, tumbling in flight.
- rigid body - Euler angles
Rotary work. Moment of power
Consider the work done during the rotation of a material point around a circle under the action of the projection of the acting force on the displacement (the tangential component of the force). In accordance with (3.1) and Fig. 4.4, passing from the parameters of translational motion to the parameters of rotational motion (dS = Rdcp)
Here, the concept of the moment of force about the axis of rotation OOi is introduced as the product of the force F s on the shoulder of force R:
As can be seen from relation (4.8), moment of force in rotational motion is analogous to force in translational motion, since both parameters when multiplied by analogues dcp and dS give work. Obviously, the moment of force must also be specified vectorially, and with respect to the point O, its definition is given through the vector product and has the form
Finally: work during rotational motion is equal to the scalar product of the moment of force and the angular displacement:
Kinetic energy during rotational motion. Moment of inertia
Consider an absolutely rigid body rotating about a fixed axis. Let's mentally divide this body into infinitely small pieces with infinitely small sizes and masses mi, m2, Shz..., located at a distance R b R 2 , R3 ... from the axis. We find the kinetic energy of a rotating body as the sum of the kinetic energies of its small parts
where Y is the moment of inertia of a rigid body, relative to a given axis OOj.
From a comparison of the formulas for the kinetic energy of translational and rotational motions, it can be seen that moment of inertia in rotational motion is analogous to mass in translational motion. Formula (4.12) is convenient for calculating the moment of inertia of systems consisting of individual material points. To calculate the moment of inertia of solid bodies, using the definition of the integral, we can transform (4.12) to the form
It is easy to see that the moment of inertia depends on the choice of axis and changes with its parallel translation and rotation. We present the values of the moments of inertia for some homogeneous bodies.
From (4.12) it is seen that moment of inertia of a material point equals
where t- point mass;
R- distance to the axis of rotation.
It is easy to calculate the moment of inertia for hollow thin-walled cylinder(or a special case of a cylinder with a small height - thin ring) radius R about the axis of symmetry. The distance to the axis of rotation of all points for such a body is the same, equal to the radius and can be taken out from under the sign of the sum (4.12):
solid cylinder(or a special case of a cylinder with a small height - disk) radius R to calculate the moment of inertia about the axis of symmetry requires the calculation of the integral (4.13). The mass in this case is, on average, concentrated somewhat closer than in the case of a hollow cylinder, and the formula will be similar to (4.15), but a coefficient less than one will appear in it. Let's find this coefficient.
Let a solid cylinder have a density R and height h. Let's break it down into
hollow cylinders (thin cylindrical surfaces) thick dr(Fig. 4.5) shows a projection perpendicular to the axis of symmetry). The volume of such a hollow cylinder of radius G is equal to the surface area multiplied by the thickness: 
weight: 
and the moment
inertia according to (4.15): Total moment
of inertia of a solid cylinder is obtained by integrating (summing) the moments of inertia of hollow cylinders: 
. Considering that the mass of a solid cylinder is related to
density formula t = 7iR 2 hp we finally have the moment of inertia of a solid cylinder:
Similarly searched moment of inertia of a thin rod length L and the masses t, if the axis of rotation is perpendicular to the rod and passes through its middle. Let us split such a rod in accordance with Fig. 4.6
into thick pieces dl. The mass of such a piece is dm=m dl/L, and the moment of inertia according to Paul
The new moment of inertia of a thin rod is obtained by integrating (summing) the moments of inertia of the pieces: 
If m.t. rotates in a circle, then a force acts on it, then when turning through a certain angle, elementary work is performed:
(22)
If the acting force is potential, then
then (24)
Rotating power
Instantaneous power developed during rotation of the body:
Kinetic energy of a rotating body
Kinetic energy of a material point. Kinetic energy sis of material points 
. Because , we obtain the expression for the kinetic energy of rotation:
In flat motion (the cylinder rolls down an inclined plane), the total speed is:
where is the speed of the center of mass of the cylinder.
The total is equal to the sum of the kinetic energy of the translational motion of its center of mass and the kinetic energy of the rotational motion of the body relative to the center of mass, i.e.:
(28)
Conclusion:
And now, having considered all the lecture material, let's summarize, compare the quantities and equations of the rotational and translational motion of the body:
| translational movement | rotational movement | ||
| Weight | m | Moment of inertia | I |
| Way | S | Angle of rotation | |
| Speed | Angular velocity | ||
| Pulse | angular momentum | ||
| Acceleration | Angular acceleration | ||
| Resultant of external forces | F | The sum of the moments of external forces | M |
| Basic equation of dynamics | Basic equation of dynamics | ||
| Work | fds | Rotation work | |
| Kinetic energy | Kinetic energy of rotation |
Appendix 1:
A person stands in the center of the Zhukovsky bench and rotates along with it by inertia. Rotation frequency n 1 \u003d 0.5 s -1 . Moment of inertia j o human body relative to
relative to the axis of rotation is 1.6 kg m 2. In arms outstretched to the sides, a person holds a kettlebell with a mass m=2 kg each. Distance between weights l 1 \u003d l.6 m. Determine the speed n 2 , benches with a person when he puts his hands down and the distance l 2 between the weights will be equal to 0.4 m. Neglect the moment of inertia of the bench.
Symmetry properties and conservation laws.
Energy saving.
The conservation laws considered in mechanics are based on the properties of space and time.
The conservation of energy is associated with the homogeneity of time, the conservation of momentum with the homogeneity of space, and, finally, the conservation of angular momentum is associated with the isotropy of space.
We start with the law of conservation of energy. Let the system of particles be in constant conditions (this takes place if the system is closed or subject to a constant external force field); connections (if any) are ideal and stationary. In this case time, due to its homogeneity, cannot enter explicitly into the Lagrange function. Really homogeneity means the equivalence of all moments of time. Therefore, the replacement of one moment of time by another without changing the values of coordinates and particle velocities should not change the mechanical properties of the system. This is of course true if the replacement of one moment of time by another does not change the conditions in which the system is located, that is, if the external field is independent of time (in particular, this field may be absent).
So for a closed system located in a closed force field, .
Work and power during rotation of a rigid body.
Let's find an expression for work during the rotation of the body. Let the force be applied at a point located at a distance from the axis - the angle between the direction of the force and the radius vector . Since the body is absolutely rigid, the work of this force is equal to the work expended on turning the whole body. When the body rotates through an infinitely small angle, the point of application passes the path and the work is equal to the product of the projection of the force on the direction of displacement by the displacement value:
The modulus of the moment of force is equal to:
then we get the following formula for calculating the work:
Thus, the work during rotation of a rigid body is equal to the product of the moment of the acting force and the angle of rotation.
Kinetic energy of a rotating body.
Moment of inertia mat.t. called physical the value is numerically equal to the product of the mass of mat.t. by the square of the distance of this point to the axis of rotation. W ki \u003d m i V 2 i / 2 V i -Wr i Wi \u003d miw 2 r 2 i / 2 \u003d w 2 / 2 * m i r i 2 I i \u003d m i r 2 i moment of inertia of a rigid body is equal to the sum of all mat.t I=S i m i r 2 i the moment of inertia of a rigid body is called. physical value equal to the sum of the products of mat.t. by the squares of the distances from these points to the axis. W i -I i W 2 /2 W k \u003d IW 2 /2
W k \u003d S i W ki moment of inertia during rotational motion yavl. analogue of mass in translational motion. I=mR 2 /2
21. Non-inertial reference systems. Forces of inertia. The principle of equivalence. Equation of motion in non-inertial frames of reference.
Non-inertial frame of reference- an arbitrary reference system that is not inertial. Examples of non-inertial frames of reference: a frame moving in a straight line with constant acceleration, as well as a rotating frame.
When considering the equations of motion of a body in a non-inertial frame of reference, it is necessary to take into account additional inertial forces. Newton's laws are valid only in inertial frames of reference. In order to find the equation of motion in a non-inertial frame of reference, it is necessary to know the laws of transformation of forces and accelerations during the transition from an inertial frame to any non-inertial one.
Classical mechanics postulates the following two principles:
time is absolute, that is, the time intervals between any two events are the same in all arbitrarily moving frames of reference;
space is absolute, that is, the distance between any two material points is the same in all arbitrarily moving frames of reference.
These two principles make it possible to write down the equation of motion of a material point with respect to any non-inertial frame of reference in which Newton's First Law is not fulfilled.
The basic equation of the dynamics of the relative motion of a material point has the form:
where is the mass of the body, is the acceleration of the body relative to the non-inertial frame of reference, is the sum of all external forces acting on the body, is the portable acceleration of the body, is the Coriolis acceleration of the body.
This equation can be written in the familiar form of Newton's Second Law by introducing fictitious inertial forces:
Portable inertia force
Coriolis force
inertia force- fictitious force that can be introduced in a non-inertial frame of reference so that the laws of mechanics in it coincide with the laws of inertial frames.
In mathematical calculations, the introduction of this force occurs by transforming the equation
F 1 +F 2 +…F n = ma to the form
F 1 + F 2 + ... F n –ma = 0 Where F i is the actual force, and –ma is the “force of inertia”.
Among the forces of inertia are the following:
simple force of inertia;
centrifugal force, which explains the tendency of bodies to fly away from the center in rotating frames of reference;
the Coriolis force, which explains the tendency of bodies to deviate from the radius during radial motion in rotating frames of reference;
From the point of view of general relativity, gravitational forces at any point are the forces of inertia at a given point in Einstein's curved space
Centrifugal force- the force of inertia, which is introduced in a rotating (non-inertial) frame of reference (in order to apply Newton's laws, calculated only for inertial FRs) and which is directed from the axis of rotation (hence the name).
The principle of equivalence of forces of gravity and inertia- a heuristic principle used by Albert Einstein in deriving the general theory of relativity. One of the options for his presentation: “The forces of gravitational interaction are proportional to the gravitational mass of the body, while the forces of inertia are proportional to the inertial mass of the body. If the inertial and gravitational masses are equal, then it is impossible to distinguish which force acts on a given body - gravitational or inertial force.
Einstein's formulation
Historically, the principle of relativity was formulated by Einstein as follows:
All phenomena in the gravitational field occur in exactly the same way as in the corresponding field of inertial forces, if the strengths of these fields coincide and the initial conditions for the bodies of the system are the same.
22. Galileo's principle of relativity. Galilean transformations. Classical velocity addition theorem. Invariance of Newton's laws in inertial frames of reference.
Galileo's principle of relativity- this is the principle of physical equality of inertial reference systems in classical mechanics, which manifests itself in the fact that the laws of mechanics are the same in all such systems.
Mathematically, Galileo's principle of relativity expresses the invariance (invariance) of the equations of mechanics with respect to transformations of the coordinates of moving points (and time) when moving from one inertial frame to another - Galilean transformations.
Let there be two inertial frames of reference, one of which, S, we will agree to consider as resting; the second system, S", moves with respect to S with a constant speed u as shown in the figure. Then the Galilean transformations for the coordinates of a material point in the systems S and S" will have the form:
x" = x - ut, y" = y, z" = z, t" = t (1)
(the primed quantities refer to the S frame, the unprimed quantities refer to S). Thus, time in classical mechanics, as well as the distance between any fixed points, is considered the same in all frames of reference.
From Galileo's transformations, one can obtain the relationship between the velocities of a point and its accelerations in both systems:
v" = v - u, (2)
a" = a.
In classical mechanics, the motion of a material point is determined by Newton's second law:
F = ma, (3)
where m is the mass of the point, and F is the resultant of all forces applied to it.
In this case, forces (and masses) are invariants in classical mechanics, i.e., quantities that do not change when moving from one frame of reference to another.
Therefore, under Galilean transformations, equation (3) does not change.
This is the mathematical expression of the Galilean principle of relativity.
GALILEO'S TRANSFORMATIONS.
In kinematics, all frames of reference are equal to each other and motion can be described in any of them. In the study of movements, sometimes it is necessary to move from one reference system (with the coordinate system OXYZ) to another - (О`Х`У`Z`). Let's consider the case when the second frame of reference moves relative to the first uniformly and rectilinearly with the speed V=const.
To facilitate the mathematical description, we assume that the corresponding coordinate axes are parallel to each other, that the velocity is directed along the X axis, and that at the initial time (t=0) the origins of both systems coincide with each other. Using the assumption, which is fair in classical physics, about the same flow of time in both systems, it is possible to write down the relations connecting the coordinates of some point A(x, y, z) and A (x`, y`, z`) in both systems. Such a transition from one reference system to another is called the Galilean transformation):
OXYZ O`X`U`Z`
x = x` + V x t x` = x - V x t
x = v` x + V x v` x = v x - V x
a x = a` x a` x = a x
The acceleration in both systems is the same (V=const). The deep meaning of Galileo's transformations will be clarified in dynamics. Galileo's transformation of velocities reflects the principle of independence of displacements that takes place in classical physics.
Addition of speeds in SRT
The classical law of addition of velocities cannot be valid, because it contradicts the statement about the constancy of the speed of light in vacuum. If the train is moving at a speed v and a light wave propagates in the car in the direction of the train, then its speed relative to the Earth is still c, but not v+c.
Let's consider two reference systems.
In system K 0 the body is moving at a speed v one . As for the system K it moves at a speed v 2. According to the law of addition of speeds in SRT: 
If a v<<c and v 1 << c, then the term can be neglected, and then we obtain the classical law of addition of velocities: v 2 = v 1 + v.
At v 1 = c speed v 2 equals c, as required by the second postulate of the theory of relativity: 
At v 1 = c and at v = c speed v 2 again equals speed c. 
A remarkable property of the law of addition is that at any speed v 1 and v(not more c), resulting speed v 2 does not exceed c. The speed of movement of real bodies is greater than the speed of light, it is impossible.
Addition of speeds
When considering a complex motion (that is, when a point or body moves in one frame of reference, and it moves relative to another), the question arises about the relationship of velocities in 2 frames of reference.
classical mechanics
In classical mechanics, the absolute velocity of a point is equal to the vector sum of its relative and translational velocities:
In plain language: The speed of a body relative to a fixed frame of reference is equal to the vector sum of the speed of this body relative to a moving frame of reference and the speed of the most mobile frame of reference relative to a fixed frame.
