GENERAL PHYSICS COURSE
1. Savelyev IV "The course of general physics" V.1.2.3.
PHYSICAL BASIS OF MECHANICS
§1 The mechanical motion
The elementary view of a motion in the nature is the mechanical motion, consisting in change of a relative positioning of bodies or their parts in space eventually. The section of physics which is engaged in studying of laws of a mechanical motion, is termed as a mechanics.
Distinguish the classical mechanics, when velocities of macroscopical bodies of essentially less light speed. The classical mechanics is grounded on Newton's laws, therefore it often term as a Newtonian mechanics. Motions of bodies with velocities close to light speed it is studied in a relativistic mechanics, and laws of a motion of microparticles in a quantum mechanics.
The classical mechanics consists of three basic sections – a statics, kinematics and dynamics. The statics – studies laws of a composition of forces and a requirement of balance of bodies. The Kinematics (motion) – gives the mathematical description of a motion of bodies without reason causing this motion. Dynamics – studies a motion of bodies taking into account forces operating on them.
§2 Reference system. The material point.
Displacement, path, trajectory.
The motion in the mechanic terms change of a relative positioning of bodies. For the description of a motion of bodies it is necessary to choose prestressly a reference system, i.e. to choose one or several bodies which conventionally are accepted to immobile, and to them to relate any coordinate system and hours.
Perfectly rigid body terms a body which strain in the conditions of the given problem can be neglected. The distance between any two points perfectly rigid body does not change at any interactions.The body, in relation to which the motion of other bodies is considered, is termed as a body frame.
The rectangular, Cartesian frame formed by three crossly perpendicular axes X, Y, Z is most often used.Unit vector along these axes are termed orts -. They lay out the origin of O. Position of a point P is characterized by the radius vector ,connecting the origin O with a point of P .
X, Y, Z – Cartesian coordinates of the point P or projections of the radius vector on the respective axes of co-ordinates. Character of a motion of a body in space will be set, if we know, how change in time of co-ordinate or its radius vector, i.e. dependences x = x (t) ; y = y (t); z = z(t) will be determined
Solving a physical problem some factors which in the given problem not essential, neglect, for example, it is often possible to neglect the sizes of the body which motions it is studied.
The body which sizes in the conditions of the given problem can be neglected, is termed as the material point.
Line, described by a material point in its motion in space, called the trajectory. The distance between two point position, measured along a path called the path traveled by the body (A path – trajectory length.)
Vector between the initial position of the body and the end position, called the displacement vector.
ABCD – a trajectory
|ABCD| - a path
- displacement vector
Depending on the trajectory shape distinguish a rectilinear and curvilinear motion of a point.
If the body trajectory represents a straight line, a motion – rectilinear, a curve – curvilinear.
Besides distinguish translational and a rotary motion.
Average speed on any part of the trajectory is the ratio of the increment of the radius vector of a point in the time interval t + Δt to its duration Δt.
(The average velocity of the body in any part of the trajectory is the ratio of the length S of the site at the time t, during which the body passed this site)If for the sites of any length taken in various places of a trajectory, this relation is identical, velocity of a body along a trajectory is constant also such motion is termed as the uniform.
Speed v(instantaneous velocity) point is called a vector quantity ,equal to the first time derivative of the radius vector of the viewed point
(Velocity of a point at time t is equal to the limit of the average speed vav at Δt → 0)
In general, the path S is different from the module move | Δr |. Equally, if we consider the way dS, passable point for a small period of time dt, then dS = | dr |. Therefore the modulus of the velocity vector is the first derivative of the path length of the time.
Average ground speed of uneven movement of the point on the section of its trajectory is called a scalar quantity equal to the ratio of the length Vav of this section, the trajectory to the duration Δt of its passage point
Average path velocity of a non-uniform motion of a point on the section of its trajectory is called scalar value Vav equal to the relation of length of this section a trajectory, to duration Δt passages by its point
It is possible to present a velocity vector in a view
projection of the vector on the axes
The vector of velocity of a point is guided on a tangent to a trajectory towards a motion as well a vector of small displacement of a point for all time interval dt (a vector that is tangent to be from the physical meaning of the first derivative - is tangent to the graph of the function indicates the velocity of motion at time t).
We calculate the path the body during the time t1 - t2 in the case of non-uniform motion. Let's break a time interval t1 - t2 on N small equal intervals. The entire path traversed by the body can be found by adding all the basic ways
If that we find value S: