llecture on physics 1- 2 1 kunakov sk
Post on 10-Apr-2018
213 Views
Preview:
TRANSCRIPT
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
1/26
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
2/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
3/26
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.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
4/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
5/26
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.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
6/26
Velocity
The average velocity v of an object moving through a
displacement during a time interval (t) is described by
the formula
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
7/26
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:
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
8/26
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.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
9/26
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.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
10/26
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:
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
11/26
Velocity vector
y v
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
12/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
13/26
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 (
.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
14/26
Acceleration
Kinematics of constant acceleration
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
15/26
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.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
16/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
17/26
Force
A modern statement of Newton's second law isa vector differential equation:
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
18/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
19/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
20/26
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
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
21/26
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.
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
22/26
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".
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
23/26
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).
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
24/26
Quiz
Arithmetic mean of the following
1,2,3,2 numbers is:
1. 2
2. 8
3. 10
4. 12
5. 3
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
25/26
QuizAbsolute error and standard deviation
are in the following relation:
-
8/8/2019 Llecture on Physics 1- 2 1 Kunakov SK
26/26
Quiz
top related