Physics

Mechanics.For audience from foreign students1Physics2The science of the simplest and the most common matter motion forms and their relative transformationsThe science that studies the general properties and the laws of substance and field movementsThe simplest matter motion forms are present in all the most complex forms of itA substance and a field are forms of the matterThe matterThe world around us, all that exist around us and revealed by us per sensationsThe motion is an essential matter property and its existence formThe motion is various matter changes: from the simple transfer to the most complex mentality processes3Physical Foundation of mechanicsKinematics Basis4Studies the motion laws of macroscopic bodies with velocities that are comparable with the speed of lightThe mechanics5Part of physics, which studies the motion laws and reasons that cause or change this motionClassicalRelativisticQuantum mechanicsStudies the motion laws of macroscopic bodies. Their velocities are smaller then speed of lightStudies the motion laws of microscopic bodies single atoms and elementary particlesThe branches of mechanicsKinematicsStudies the objects movement without the causes that lead to this movementsDynamicsStudies the motion laws and causes that induce and change this motionStaticsStudies equilibrium laws of bodies system

If the motion laws are known, then the equilibrium laws could be established6!!Physical models in mechanicsPhysical models are used in mechanics for describing bodies motion. This model depends on specific tasks termsMass point is a body having a mass the size of which can be disregarded in this task. It is an abstract conceptMass point system. Random macroscopic object or bodies system can be represented as a mass point system. In this system mass points interact among themselves.7Physical models in mechanicsA perfectly rigid bodyIs a body, that can not become deformed at any terms. The distance between two particles of that body remains constant at any terms.A perfectly elastic bodyBody deformation obeys the Hookes law. After the termination of external forces the body takes its original size and form.A perfectly inelastic bodyBody keeps strain state after termination of external forces.8Mechanical motionAn indication bodyThe position of moving body is determined relative to randomly selected body (indication body).Coordinate systemIs a system associated with an indication body.Base, or frameIs a combination of the indication body, the coordinate system and the clock synchronized among themselves.

9Base, or frame0zyxrzxyCartesian coordinate system xyzMechanical motionKinematic equation of mass point movement0zyxrzxyx=x(t)y=y(t)z=z(t)or

r = r (t)The position of mass point at frame is described by three coordinates x, y, z or radius-vector r. When mass point moves, its coordinates change within time (t). So this movement is described by the scalar equation system or the equivalent vector equation.10Trajectory is a line describing by moving mass point (body) relative to selected base.Depending on trajectory form there are several motion types:Rectilinear, or straight-line CurvilinearCircular motion and etc.

The trajectory form depends on a mass point motion character and a base.

11!!TrajectoryPath length and displacement vector120zyxr1r2ABrDisplacement vectorIt is a vector from the start position of the moving point to its position at this moment.s=s(t) a scalar time function.Path lengthIt is a length of path AB passed by mass point at a given period of time.

Forward motionIt is a motion, when some straight line, inflexibly connected with a moving body and drown between two random points, stays parallel to itself.In this case all body points are moving equally. Thus, the forward motion of this body can be characterized by the motion of some random body point (e.g., by body mass center motion)13AAABBBCCCRotatory motionIt is a motion, when all body points are moving in circles, which centers are lying on the equal straight line called axis of rotation.The different body points are moving differently, that is why, its rotatory motion cannot be characterized by a motion of any point.14OOKinematics of forward motion15VelocityA velocity is a vector quantity that determines, from one hand, the motion speed and from other hand, its direction at a given period of time.A mean velocity is a vector quantity that is determined by ratio of the point radius-vector increment r to the time interval t within which this increment has occurred.16OABsvrr2r1The mean velocity vector direction coincides with the direction r

VelocityOne meter per second means the velocity of forward and uniformly moving point, with which this point in 1 second shifts at a distance of 1 meter.17

AccelerationAn acceleration is a non-uniform motion characteristic that determines the velocity change rate in absolute value and in direction.A mean acceleration is a vector quantity that is determined by ratio of velocity change v to the time interval t within which this change occurred.18An instant acceleration is a vector quantity that is determined by first derivative of the velocity with time

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anavaComponents of accelerationA tangential acceleration characterizes the velocity change rate in absolute value. It is directed along the tangent to trajectory.A normal acceleration characterizes the velocity change rate in direction. It is directed to the trajectory curvature center.19

The full acceleration in curvilinear motion20

Geometric sum of the tangential and normal acceleration componentThe full acceleration absolute valueThe unit of accelerationMotion classificationaanMotion00Straight-line and uniforma = a = const0Straight-line and uniformly accelerateda = f(t)0Straight-line, with variable acceleration0constUniform, in a circle0 0Uniform and curvilinearconst 0Curvilinear and uniformly accelerateda = f(t) 0Curvilinear, with variable acceleration 21Illustration of different motion typesUniform and uniformly accelerated motion22Uniform motion (v = v0 = const)23

vv00st0st0sts0VelocityAccelerationPassed way

Uniformly accelerated motion (a = const)24

Accelerationaa0vtVelocity

0vtsvUniformly accelerated motion (a = const)25Passed way

0st

0sts0Free fallIt is a motion that body would commit only by gravity without air resistance.If body free falls from low altitude h (h