llecture on physics 1- 2 1 kunakov sk

8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK

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Length

In the physical sciences and engineering, when onespeaks of "units of length", the word "length" is

synonymous with distance. In the InternationalSystem of Units(SI), the basic unit of length is themeter and is now defined in terms of the speed oflight . The centimeter and the kilometer, derivedfrom the meter, are also commonly used units.Units used to denote distances in the vastness of

space, as in astronomy, are much longer than thosetypically used on Earth and include the astronomicalunit, the light year


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Mass

Mass is the internal property of the matter and shows itsresistance to change its speed.Mass, in physics, the quantity of matter in a body

regardless of its volume or of any forces acting on it.The term should not be confused with weight, which is themeasure of the force of gravity acting on a body. Underordinary conditions the mass of a body can be consideredto be constant; its weight, however, is not constant, sincethe force of gravity varies from place to place.

Because the numerical value for the mass of a body is thesame anywhere in the world, it is used as a basis ofreference for many physical measurements, such asdensity and heat capacity.The SI unit of mass is kilograms.


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Inertia

Inertia is the resistance of any

physical object to a change in its

state of motion or rest.

It is represented numerically by an

object's mass


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Velocity

In physics , velocity is the rate of change

of displacement (position).

It is a vector physical quantity. The scalarabsolute value(magnitude) of velocity is

speed, a quantity that is measured in

meters per seconds (m/s or ms1) when

using the SI (metric) system.


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Velocity

The average velocity v of an object moving through a

displacement during a time interval (t) is described by

the formula


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Velocity

Instantaneous velocity

The instantaneous velocity vector v of an object that haspositions r(t) at time t and r(t + t) at time t + t , can be

computed as the derivate of position:


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Velocity

Tangential and normal components of velocityvector

The angular velocity of a particle in a 2-dimensional

plane is the easiest to understand. As shown in thefigure on the right (typically expressing the angularmeasures and in radians), if we draw a line from

the origin (O) to the particle (P), then the velocityvector (v) of the particle will have a component alongthe radius (radial component, v) and a componentperpendicular to the radius (cross-radial component, v

). However, it must be remembered that the velocityvector can be also decomposed into tangential andnormal components.


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Velocity

Angular velocity

A radial motion produces no change inthe distance of the particle relative to

the origin, so for purposes of findingthe angular velocity the parallel(radial) component can be ignored.

Therefore, the rotation is completelyproduced by the tangential motion

(like that of a particle moving along a

circumference), and the angularvelocity is completely determined by

the perpendicular (tangential)component of it.


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Velocity vector

It can be seen that the rate of change of theangular position of the particle is related to the

cross-radial velocity by

Combining the above twoequations and defining the

angular velocity as =d/dt

yields:

Utilizing , the angle between vectorsv and v, or equivalently as the anglebetween vectors r and v, gives:


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Velocity vector

y v


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Angular vector velocityAs in the two dimensional case, a particle will have acomponent of its velocity along the radius from the originto the particle, and another component perpendicular tothat radius. The combination of the origin point and the

perpendicular component of the velocity defines a plane ofrotation in which the behavior of the particle (for thatinstant) appears just as it does in the two dimensionalcase. The axis of rotation is then a line normal to this plane,and this axis defined the direction of the angular velocitypseudovector, while the magnitude is the same as the

pseudoscalar value found in the 2-dimensional case. Definea unit vector which points in the direction of the angularvelocity pseudovector. The angular velocity may be writtenin a manner similar to that for two dimensions.

Velocity vector


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Acceleration

Acceleration

Average acceleration (acceleration over a length of time) isdefined as:

where v is the change in velocity and tis the interval of time

over which velocity changes.

Acceleration is the vector quantity describing the rate of change

with time of velocity.

Instantaneous acceleration (

.


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Acceleration

Kinematics of constant acceleration


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Acceleration

Angular acceleration:

The magnitude of the angular acceleration is the rate at

which the angular velocity changes with respect to time t:

The equations of translational kinematics can easily be

extended to planar rotational kinematics with simple

variable exchanges:

Here

i and

fare, respectively, the initial and final angularpositions, i and fare, respectively, the initial and final

angular velocities, and is the constant angular

acceleration. Although position in space and velocity in

space are both true vectors (in terms of their properties

under rotation), as is angular velocity, angle itself is not a

true vector.


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Force

A a force is any influence that causes a free body toundergo an accelletion. Force can also be described by

intuitive concepts such as a push or pull that can cause anobject with mass to change its velocity (which includes to

begin moving from a state of rest), i.e., to accelerate, orwhich can cause a flexible object to deform. A force has

both magnitude and direction, making it a vector quantity.Newtons second law: F=ma, can be formulated to state

that an object with a constant mass will accelerate inproportion to the net force acting upon and in inverseproportion to its mass, an approximation which breaks

down near the speed of light. Newton's originalformulation is exact, and does not break down: this

version states that the net force acting upon an object isequal to the rate at which its momentum changes


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Force

A modern statement of Newton's second law isa vector differential equation:


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Force

Action and Reaction

Newton's third law is a result of applying symmetry to situationswhere forces can be attributed to the presence of differentobjects. For any two objects (call them 1 and 2), Newton's thirdlaw states that any force that is applied to object 1 due to theaction of object 2 is automatically accompanied by a force appliedto object 2 due to the action of object 1


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Force

This means that in a closed system of particles, there are no

internal forces that are unbalanced. That is, action-and-reactionpairs of forces shared between any two objects in a closed system

will not cause the center of mass of the system to accelerate. The

constituent objects only accelerate with respect to each other,

the system itself remains unaccelerated . Alternatively, if an

external force acts on the system, then the center of mass will

experience an acceleration proportional to the magnitude of theexternal force divided by the mass of the system.[Combining

Newton's second and third laws, it is possible to show that the

linear momentum of a system is conserved.

Linear momentum of a closedsystem is conserved


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The angular momentum

The angular momentum L of a particle

about a given origin is defined as.

where r is the position vector of the particle relative to the

origin, p is the linear momentum of the particle, and denotes

the cross product.

As seen from the definition, the derived SIunits of angular momentum are newtonmetre seconds (Nms or kgm2s1) or jouleseconds


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The angular momentum

For an object with a fixed mass that is rotating abouta fixed symmetry axis, the angular momentum is

expressed as the product of the moment of inertiaof the object and its angular velocity vector:

where I is the moment of inertia of the object (ingeneral, a tensor quantity) and is the angular

velocity.

It is a purely geometric characteristic of the

object, as it depends only on its shape and theposition of the rotation axis. The moment of

inertia is usually denoted with the capital

letterI:It depends only on its shape and the position of the

rotation axis.


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Torque

Moment

Moment of force

Using vectors in physics

Torque, also called moment or moment of force (see the terminology below), is the tendency ofa force to rotate an object about an axis,[1] fulcrum, or pivot. Just as a force is a push or a pull, atorque can be thought of as a twist.Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel.For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque(turning force) that loosens or tightens the nut or bolt.

The terminology for this concept is not straightforward: In the US in physics, it is usually called"torque", and in mechanical engineering, it is called "moment".[2] However outside the US this variesand, in the UK for instance, most physicists will use the term "moment". In mechanical engineering,the term "torque" means something different,[3] described below. In this article, the word "torque" isalways used to mean the same as "moment".


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Torque

Moment

Moment of forceThe symbol for torque is typically ,

When it is called moment, it is commonly denotedM.

The magnitude of torque depends on three quantities:

First, the force applied;second, the length of the lever arm connecting the axis to the

point of force application;

and third, the angle between the two.

In symbols:

where

is the torque vector and is the magnitude of the torque, r is the displacement vector (a vectorfrom the point from which torque is measured to the point where force is applied), and ris the

length (or magnitude) of the lever arm vector, F is the force vector, and Fis the magnitude of theforce, denotes the cross product, is the angle between the force vector and the lever arm

vector. The length of the lever arm is particularly important; choosing this length appropriately liesbehind the operation of levers, pulleys, gears, and most other simple machines involving a

mecanical advantage.

The SI unit for torque is the newton meter (Nm).


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Quiz

Arithmetic mean of the following

1,2,3,2 numbers is:

1. 2

2. 8

3. 10

4. 12

5. 3


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QuizAbsolute error and standard deviation

are in the following relation:


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Quiz

llecture on physics 1- 2 1 kunakov sk

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