general physics i, lec 1 1 chapter (1,2). general physics i, lec 1 2 physical quantities (in...

general physics I, lec 1 1

Chapter (1,2)


Physical quantities (in mechanics)

Basic quantities : in mechanics the three fundamental quantities are length(L)

mass (M) time (t)

Derived quantities : all other physical quantities in mechanics can be expressed in term of basic quantities

Area Volume VelocityAccelerationForce MomentumWork…..…..


Systems of Units

SI units (International System of Units ): length: meter (m)

mass: kilogram (kg) time: second (s)

This system is also referred to as the mks system for meter-kilogram-second.

Gaussian unitslength: centimeter (cm)

mass: gram (g) time: second (s)

This system is also referred to as the cgs system for centimeter-gram-second.

British engineering system:

length: foot (ft) mass: slug

time: second (s)


MassThe SI unit of mass is the Kilogram, which is defined as the mass of a specific platinum-iridium alloy cylinder.

TimeThe SI unit of time is the Second, which is the time required for a cesium-133 atom to undergo 9192631770 vibrations.

LengthThe SI unit of length is Meter, which is the distance traveled by light is vacuum during a time of 1/2999792458 second.


QuantityLengthMasstime

Dimension[L=]L[M=]M

[T=]T

area[A = ]L2

volume[V=]L3

velocity [v] =L/T

Accelerationforce

[a] = L/T2

[f=]M L/T2

Dimensional Analysis

Definition: The Dimension is the qualitative nature of a physical quantity) length, mass, time .(

brackets ] [ denote the dimension or units of a physical quantity:


Idea: Dimensional analysis can be used to derive or check formulas by treating dimensions as algebraic quantities. Quantities can be added or subtracted only if they have the same dimensions, and quantities on two sides of an equation must have the same dimensions

Example(1)Using the dimensional analysis check that this equation

x = ½ at2 is correct, where x is the distance, a is the acceleration and t is the time.

L]x[ left hand side

LTT

L]at

2

1[ 2

22 right hand side

This equation is correct because the dimension of the left and right side of the equation have the same dimensions.

Solution


Example(2)Suppose that the acceleration of a particle moving in circle of radius r

with uniform velocity v is proportional to the rn and vm. Use the dimensional analysis to determine the power n and m.

The left hand side

Therefore

or

SolutionLet us assume a is represented in this expression

a = k rn vm

Where k is the proportionality constant of dimensionless unit.

The right hand side [a] = L/T2

mnm2 TLLT


Hence

n+m=1 and m=2 Therefore

n =-1

and the acceleration a is a = k r -1 v2

Problems:

1 .Show that the expression x = vt +1/2 at2 is dimensionally correct , where x is coordinate and has unit of length, v is velocity, a is acceleration and t is the time.

2 .Show that the period T of a simple pendulum is measured in time unit given by

g

l2T


Coordinate Systems and Frames of Reference

The location of a point on a line can be described by one coordinate; a point on a plane can be described by two coordinates; a point in a three dimensional volume can be described by three coordinates. In general, the number of coordinates equals the number of dimensions. A coordinate system consists of:

1 .a fixed reference point (origin)

2 .a set of axes with specified directions and scales

3 .instructions that specify how to label a point in space relative to the origin and axes


For Example: (rectangular coordinate system): (x,y) Cartesian coordinate system

Plane polar coordinates: ),r(


The relation between coordinates

rosx sinry

22 yxr

x

ytan

Furthermore, it follows that

Problem: A point is located in polar coordinate system by the coordinate and.

Find the x and y coordinates of this point, assuming the two coordinate systems have the same origin .

5.2r 35


Example (3): The Cartesian coordinates of a point are given by (x,y)= (-3.5,-2.5) meter.

Find the polar coordinates of this point .

Solution:

21636180

714.05.3

5.2

x

ytan

m3.4)5.2()5.3(yxr 2222

Note that you must use the signs of x and y to find that is in the third quadrant of coordinate system. That is not 36

216


Scalars and Vectors Scalars have magnitude only. Length, time, mass, speed and volume are examples of scalars.

Vectors have magnitude and direction. The magnitude of is written | | v Position, displacement, velocity, acceleration and force are examples of vector quantities.

Vectors have the following properties: 1 .Vectors are equal if they have the same

magnitude and direction .


4 .Multiplication or division of a vector by a scalar results in a vector for which )a (only the magnitude changes if the scalar is positive

)b (the magnitude changes and the direction is reversed if the scalar is negative .

2 .Vectors must have the same units in order for them to be added or subtracted .

3 .The negative of a vector has the same magnitude but opposite direction .


5 .Vector Addition:

The sum of two vectors, A and B, is a vector C, which is obtained by placing the initial point of B on the final point of A, and then drawing a line

from the initial point of A to the final point of B , as illustrated in figure

C = A + B

6. Subtraction of a vector is defined by adding a negative vector:

cosAB2BAR 22


7. The projections of a vector along the axes of a rectangular coordinate system are called the components of the vector. The components of a vector completely define the vector.

cosAA x

sinAA y

2y

2x )A()A(A

x

y1

A

Atan


Problem:

Problem:

general physics i, lec 1 1 chapter (1,2). general physics i, lec 1 2 physical quantities (in...

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