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Fundamental Physics Quick Revision 11th Standard 101-2b

101-2b
In this section, we cover the fundamental concept of Scalars and Vectors
First off, what is a quantity?
A quantity is a measure of certain physical events or instances that are inherently present in the natural world.
Now to this extent we ask, how do we measure these quantities?
A scalar is a physical quantity that is defined solely based on it's magnitude.A vector is a physical quantity that is defined based on both it's magnitude and it's direction.

A particle moving along a straight line can move in only two directions. We can take its motion to be positive in one of these directions and negative in the other. For a particle moving in three dimensions, however, a plus sign or minus sign is no longer enough to indicate a direction. Instead, we must use a vector.

A vector has magnitude as well as direction, and vectors follow certain (vector) rules of combination, which we examine in this chapter. A vector quantity is a quantity that has both a magnitude and a direction and thus can be represented with a vector. Some physical quantities that are vector quantities are displacement, velocity, and acceleration. You will see many more throughout this book, so learning the rules of vector combination now will help you greatly in later chapters.

Not all physical quantities involve a direction. Temperature, pressure, energy, mass, and time, for example, do not “point” in the spatial sense. We call such quantities scalars, and we deal with them by the rules of ordinary algebra. A single value, with a sign (as in a temperature of 40°F), specifies a scalar.

The simplest vector quantity is displacement, or change of position. A vector that represents a displacement is called, reasonably, a displacement vector. (Similarly, we have velocity vectors and acceleration vectors.) If a particle changes its position by moving from A to B in, we say that it undergoes a displacement from A to B, which we represent with an arrow pointing from A to B. The arrow specifies the vector graphically. To distinguish vector symbols from other kinds of arrows in this book, we use the outline of a triangle as the arrowhead.



The arrows from A to B, from A to B , and from A to B have the same magnitude and direction. Thus, they specify identical displacement vectors and represent the same change of position for the particle. A vector can be shifted without changing its value if its length and direction are not changed.
The displacement vector tells us nothing about the actual path that the particle takes. For example, all three paths connecting points A and B cor- respond to the same displacement vector, that of the Displacement vectors represent only the overall effect of the motion, not the motion itself.

To elaborate, in order for a quantity to be considered a vector, the physical or numerical values considered to define it, it must be accompanied by a secondary set of value that provide the necessary data on the direction or orientation of that quantity in physical space.The fundamental quantities, are all scalar quantities i.e Mass, Length, Time etc.
The derived quantities, such as Force, Displacement, Velocity etc. are vectors.The difference is more imperative when considering specific quantities w.r.t the world co-oordinate systems, so as to improve upon anything physical.

Fundamental Physics Quick Revision 11th Standard 101-2a

101-2a

This part deals with the essentials of the three main kinematic parameters and the equations pertaining to motion.

The world, and everything in it, moves. Even seemingly stationary things, such as a roadway, move with Earth’s rotation, Earth’s orbit around the Sun, the Sun’s or- bit around the center of the Milky Way galaxy, and that galaxy’s migration relative to other galaxies. The classification and comparison of motions (called kinematics) is often challenging. What exactly do you measure, and how do you compare?

Before we attempt an answer, we shall examine some general properties of motion that is restricted in three ways.

1. The motion is along a straight line only. The line may be vertical, horizontal, or slanted, but it must be straight. 


2. Forces(pushes and pulls)cause motion. In this chapter we discuss only the motion itself and changes in the motion. Does the moving object speed up, slow down, stop, or reverse direction? If the motion does change, how is time involved in the change? 


3. The moving object is either a particle (by which we mean a point-like object such as an electron) or an object that moves like a particle (such that every portion moves in the same direction and at the same rate). A stiff pig slipping down a straight playground slide might be considered to be moving like a par- ticle; however, a tumbling tumbleweed would not. 


The three main kinematic parameters are:

Parameter            Standard unit of measure

Displacement                         m
Velocity                                 m/s
Acceleration                          m/s²

As you may well know, all three above quantities are vector quantities, meaning that they have both magnitude and direction.

It is also to be noted that all three of these quantities are incremental differentials of the same physical quantity, displacement, with respect to time.

To elaborate,

Displacement is the shortest distance between two points. Its magnitude is in meters, and relative direction can be either along the positive direction on the Cartesian plane or along the negative direction on the Cartesian plane.

It's variation, i.e differential, with respect to time renders the result we call velocity.
The rate of change of displacement with respect to time is therefore what is known as velocity.

The same directional parameters as those of the displacement that determined it, will play a part in determining the direction of the velocity.

The rate of change of velocity, following from the case of velocity will also derive it's direction from the former. This is acceleration.

There are 4 fundamental equations of motion connecting the three quantities and time:

Where v is final velocity, u is initial velocity, a is acceleration, s is displacement and t is time

Fundamental Physics Quick Revision 11th Standard 101-1a

101-1a

Here are some fundamental mathematical basics of 11th Standard Physics for your quick reference

This one 101-1a will cover all the basic formulae you will need to solve your Kinematics problems and some for basic unit conversions.

SI Prefixes*

Factor  Prefix  Symbol
1024    yotta        Y
1021    zetta         Z
1018    exa           E
1015    peta          P
1012    tera          T
109      giga         G
106      mega       M
103      kilo          k
102      hecto        h
101      deka        da

Factor   Prefix    Symbol
10–1       deci        d
10–2       centi       c
10–3       milli       m
10–6       micro     mu 
10–9       nano       n
10–12     pico        p
10–15     femto      f
10–18     atto         a
10–21     zepto      z
10–24     yocto      y

*In all cases, the first syllable is accented, as in ná-no-mé-ter.

 

 

Trigonometric Identities:

Reciprocal identities

Pythagorean Identities

Quotient Identities

Co-Function Identities

Even-Odd Identities

Sum-Difference Formulas

Double Angle Formulas

Power-Reducing/Half Angle Formulas

Sum-to-Product Formulas

Product-to-Sum Formulas

Basic Derivatives and Integrals:

 

 

Newton's generalized binomial theorem

In this generalization, the finite sum is replaced by an infinite series. In order to do this, one needs to give meaning to binomial coefficients with an arbitrary upper index, which cannot be done using the usual formula with factorials. However, for an arbitrary number r, one can define

where  is the Pochhammer symbol, here standing for a falling factorial. This agrees with the usual definitions when r is a nonnegative integer. Then, if x and y are real numbers with |x| > |y|, and r is any complex number, one has

When r is a non negative integer, the binomial coefficients for k > r are zero, so this equation reduces to the usual binomial theorem, and there are at most r + 1 nonzero terms. For other values of r, the series typically has infinitely many nonzero terms.
For example, with r = 1/2 gives the following series for the square root:

Taking , the generalized binomial series gives the geometric series formula, valid for :

More generally, with r = −s:

So, for instance, when ,

 

Vector Product of Vectors

The vector product and the scalar product are the two ways of multiplying vectors which see the most application in physics and astronomy. The magnitude of the vector product of two vectors can be constructed by taking the product of the magnitudes of the vectors times the sine of the angle (<180 degrees) between them. The magnitude of the vector product can be expressed in the form:  and the direction is given by the right-hand rule. If the vectors are expressed in terms of unit vectors i, j, and k in the x, y, and z directions, then the vector product can be expressed in the rather cumbersome form:
 

Vector Product, Determinant Form

The vector product is compactly stated in the form of a determinant which for the 3x3 case has a convenient evaluation procedure:
Once the scheme for determinant evaluation is familiar, this is a convenient way to reconstruct the expanded form:

Fundamental Physics Quick Revision 11th Standard 101-1b

101-1b

This part of the portion covers a summary of the fundamentals of units and measurements.

Units and measurements form the backbone of all things Physics as they provide both the qualitative and quantitative aspects of Physics meaning and understanding.

Facts considered, there are 7 fundamental quantities, i.e

Mass

Length

Time

Temperature

Current
Amount of substance

Luminous intensity 

Each of these have their own SI unit, namely

Mass - Kilogram (kg)

Length - Meter (m)

Time - Second (s)

Temperature - Degree Kelvin (K)

Current - Ampere (A)

Amount of substance - Avogadro Mole (mol)

Luminous intensity - Candela (c)

In this section, we discuss the fundamental quantities necessary for basic statics and kinematics, i.e

Length, Time and Mass.

Length 

The meter came to be defined as the distance between two fine lines engraved near the ends of a platinum – iridium bar, the standard meter bar, which was kept at the International Bureau of Weights and Measures near Paris. Accurate copies of the bar were sent to standardizing laboratories throughout the world. These secondary standards were used to produce other, still more accessible standards, so that ultimately every measuring device derived its authority from the standard meter bar through a complicated chain of comparisons. 
 
The meter was redefined as the distance traveled by light in a specified time interval.
In the words of the 17th General Conference on

Weights and Measures: 

This time interval was chosen so that the speed of light c is exactly c 299 792 458 m/s.
Measurements of the speed of light had become extremely precise, so it made sense to adopt the speed of light as a defined quantity and to use it to redefine the meter. Table 1-3 shows a wide range of lengths, from that of the universe (top line)

The meter is the length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second. 

Time 

Time has two aspects. For civil and some scientific purposes, we want to know the time of day so that we can order events in sequence. In much scientific work, we want to know how long an event lasts. Thus, any time standard must be able to answer two questions: “When did it happen?” and “What is its duration?” 

To meet the need for a better time standard, atomic clocks have been developed.

The 13th General Conference on Weights and Measures in 1967 adopted a standard second based on the cesium clock:  

One second is the time taken by 9 192 631 770 oscillations of the light (of a specified wavelength) emitted by a cesium-133 atom.

Atomic clocks are so consistent that, in principle, two cesium clocks would have to run for 6000 years before their readings would differ by more than 1 s. Even such accuracy pales in comparison with that of clocks currently being developed; their precision may be 1part in 1018—that's, 1 in 1x1018 s(which is about 3x1010 y).

Mass

The SI standard of mass is a platinum–iridium cylinder (Fig. 1-3) kept at the International Bureau of Weights and Measures near Paris and assigned, by international agreement, a mass of 1 kilogram. Accurate copies have been sent to standardizing laboratories in other countries, and the masses of other bodies can be determined by balancing them against a copy. Table 1-5 shows some masses expressed in kilograms, ranging over about 83 orders of magnitude.  

Class 11 – Science - Anatomy of flowering plants

In Science, I always have difficulties in this subject that too in Botany. But I don’t want people to get scared of this subject as it is very interesting and you can learn it from our day to day life. You learned Morphology of flowering plants. Today I am taking up the anatomy of the flowering plants. The monocot, Dicot and Tricot are the terms which needs to keep in mind. The epidermis is the upper portion of the stem while the mesophyll is the middle ne and the vascular system is the bundles present in leaves and stems.

You will find different topics of Class 11 Science – Biology. Today we will take up the questionnaires of Morphology of flowering plants. This solutions are created by experts of the subject. They help many students helps prepare for their exam and score marks. This not only will help prepare in the respective exams but also will help in preparation of competitive exams as well.

The solutions included in this questionnaires are very simple to understand and I make sure this will help understand as I try to describe in detail. You may find a series of this topics in my blogs every day. So keep reading and follow the posts with your valuable comments.