May 21, 2020

VECTORS – 1 (MASTER ADVANCED PHYSICS)

MASTER ADVANCED PHYSICS
(For all Top Exams) 

VECTORS – 1

Vectors and Scalars 

What are vectors? Vectors are those quantities that have both magnitude and direction. Scalars are those quantities that have ONLY magnitude. 

Let us take two examples to make our concept of vectors totally clear. 

Let us take force and temperature. 

Now suppose there are two or more forces acting on a body. Is it not important IN WHICH DIRECTION they are acting? 

If two equal forces act in exactly opposite directions, the body will not move. 

If they act in the same direction, the body will move with both forces added up. 

The force might act at different angles too. Is it not? 

Definitely, by nature force has both magnitude and direction. Such quantities are called as vectors. 

Other examples of vectors are Velocity, Momentum, Displacement etc. In each of them, the direction becomes important. 

Now, let us take temperature. In any direction, the temperature remains constant. There is nothing like a direction. Such quantities, where direction is not inherent to the quantity and only magnitude is there, we call scalars. 

Other examples of scalar quantities are mass, distance, speed, work, energy..etc 

What is Vector Algebra? 

Now, since vector quantities have both magnitude and direction, how do we ADD or SUM UP or find what is called the RESULTANT of two vectors. 

In real life, suppose we have many forces acting on a body, at different angles, how do we predict beforehand, what the RESULTANT force would be, and hence finally how the body would move? 

It cannot be just addition of magnitudes because DIRECTION also is involved. So, we have concepts of vector algebra and with these concepts, we can add/sum up vector quantities keeping direction in mind also. 

We also have PRODUCTS, dot product and cross product, some special concepts that we will see in the later units. 

To do all these things, we need some simple and clear definitions and symbols that we use in vector algebra. In the next section we will study them. 

May 18, 2020

KINEMATICS - 3 (MASTER ADVANCED PHYSICS)

KINEMATICS - 3 (MASTER ADVANCED PHYSICS)
MASTER ADVANCED PHYSICS
(For all Top Exams) 

Video – 3 
KINEMATICS - 3

Motion under Gravity 

We must remember that even in straight line motion, we have positive and negative directions for velocity, acceleration and displacement 

a=g = 9.8 m/s/s 

1. Body dropped from a height – h 

Equations 

U= 0, v= v, S= H, t= t (time of flight) 

a= +g 

So, V= g*t 

H= ½ gt2 

v2= 2*g*H 

Time of fall = t = root of 2h/g 

Velocity with which it reaches the ground = v= root of 2gh 

2. When a body is thrown upwards with a velocity – u 

Equations – upwards – positive , downwards – negative 

U= u, v= 0 , a= -g, s= H, t= t 

0= u-gt 

h = ut – ½ gt2 

U2 = 2*g*h 

So, 

Maximum height reached = h= u2/2g 

Time of ascent= time of descent = u/g 

Total time in flight = 2u/g 

3. Body projected from a tower of height H with velocity – u 

Equations – upward is positive 

Downward is negative 

U= u, s= -h(height of the tower is displacement) , t= t , v= -v, g= g 

U2- V2= -2gh 

So, 

Velocity with which it reaches the ground = v = root of u2 +2gh 

Total time taken to reach the foot of tower = time to reach the top + time of fall 

= u/g + root of (u2 +2gh) / g

KINEMATICS-2 (MASTER ADVANCED PHYSICS)

KINEMATICS-2 (MASTER ADVANCED PHYSICS)
MASTER ADVANCED PHYSICS 
(For all Top Exams) 

Video – 2 
KINEMATICS – 2

Acceleration –

Change in velocity

Uniform acceleration

Rate of change in velocity is constant

Change in Velocity in one second.

V= 0 t= 0

V= 10 t= 1

V= 20 t= 2

V= 30 t=3

A = 10m/s /s

Equations of motion for uniformly accelerating body

U, v, a, S, t

V – u / t = a or v = u + at

S = ut + ½ a t*t

V2 – u2 = 2as

Derivation of the three equations

V= u + at is by definition true

(U + v) / 2 = average velocity = s / t

Ut + vt = 2s

Ut + (U + at)t = 2s

Ut + ut + at 2 = 2s

Dividing by 2

S = ut + ½ at2

With the first two equations we can get

V2 – u2 = 2as

by simple substitution

Displacement – time graph for uniformly accelerated motion

Graph – parabola


Velocity – time graph for uniformly accelerated motion

Graph – slanted straight line


May 17, 2020

KINEMATICS-1 (MASTER ADVANCED PHYSICS)

KINEMATICS-1 (MASTER ADVANCED PHYSICS)

Master Advanced Physics 
(For all Top Exams) 

Video – 1 
Kinematics – 1 

Statics – 

Study of bodies when not in motion 

Kinematics – 

Study of bodies when in motion but without considering the forces and the causes of motion 

Dynamics – 

Study of motion of bodies while considering the forces 

Rest and motion 

Motion in one Dimension 

Motion in 2 Dimensions 

Motion in 3 Dimensions 

Distance and Displacement 

Distance is the actual distance traveled by a body 

Displacement is the shortest / straight line distance covered by a body 

Speed and Velocity – 

Speed is distance covered in one second 

Velocity is displacement covered in one second 

Speed = d / t ……. Velocity = S / t 


Average speed and instantaneous speed 

Average speed = TOTAL distance / Total time 

Instantaneous speed is exactly speed at that point/moment of time 


Average velocity and Instantaneous velocity – 

Average Velocity = TOTAL displacement / Total time 

Instantaneous Velocity is exactly velocity at that point/moment of time 

Uniform motion in a straight line 

Position time graph 

Velocity time graph

Position time graph 




Velocity time graph


WILLIAM BLAKE AND HIS POEM TYGER


WILLIAM BLAKE AND HIS POEM TYGER


William Blake – His Life and Genius 

William Blake was born on the 28th of November, 1757, in London and died on the August of 1827. He was a great visionary poet, artist and engraver and is regarded as one of the greatest Romantic poets, but with very unique gifts of vision, spirituality, originality and intense seeking of truth and meaning. 

He was the author of the following famous books. 

Songs of innocence (1789) 

Songs of Experience (1794) 

Visions of the Daughters of Albion (1793) 

The first book of Urizen (1794) 

Milton (1804) among others. 

These works he etched, printed coloured, stitched, and sold, with the assistance of his devoted wife, Catherine. Among his best known lyrics today are “The Lamb,” “The Tyger,” “London,” and the “Jerusalem” lyric from Milton, which has become a kind of second national anthem in Britain. 

Blake was born over his father’s modest hosiery shop at 28 Broad Street, Golden Square, London. His parents were James Blake (1722–84) and Catherine Wright Armitage Blake (1722–92). 

His father was his mother’s second husband. 

He had a distinct and very deeply influential Christian upbringing. He is reported to having seen angels and god, and saints while awake. Such visions came from his burning combination of secularism, the desire to SEE things by himself, and belief in God and paradise. 

He was regarded as mad in his lifetime, but by the 21st century he has been hailed, in fact, as the greatest of Romantic poets. 

He did not have children and he had an extremely devoted wife, Catherine. He had to struggle for a living. He had an intense desire to be an artist full time, and had shown tremendous talent early on. But, due to his finances, he could not become an artist and, instead, became a skilled engraver. 

He took to writing and he himself made his own books beautifully engraved, etched and bound by his own hands. 

He wrote marvelous poems but due to the strange character and extreme originality of his works, he could not get the recognition he deserved. In fact, people sadly dismissed his thinking as a kind of madness. 

He died at the age of 69, in August 22, 1827. 

Social and Political Background and Romanticism 

The 1700 – 1800 years were turbulent, intellectually stimulating and intensely creative and those years witnessed two great revolutions, the American and French revolutions. 

They were years of very deep transition from long held tradition and habit of faith and servility to the newly emerging scientific and enlightening outlook. 

It had all the passion, suffering, intensity, questioning, confusions, anarchism of a transition, yet, it was a period where man was being finally liberated from the shackles of religion after long ages of being ruled by religious authority and leading dull and dry lives. 

Great thinkers and philosophers emerged in this period and the greatest of literary movements was that of ROMANTICISM. 

This movement had great writers, like Byron, Keats, Victor Hugo, Wordsworth and also Blake and many others. 

Each was very unique but all had a single thing in common- a deep and intense concern as to the meaning of life, the fire to pursue that question by one’s own self, to see and think and observe to truly get the truth. 

It was both liberating and agonizing!! But it changed the world. Man matured and flowered and this movement paved the way for the full emergence of the world of today that is far more enlightened than all the centuries of the past put together. 


THE MEANING AND SIGNIFICANCE OF THE POEM, TYGER 

Let us go directly to the poem, and understand the mind, heart and soul and visions, concerns, and sense of life of William Blake. 

Let us analyze, sense, and feel each line, and also let us draw out its inner meaning from the genius of expression of William Blake. 

TYGER 

Tyger! Tyger! Burning bright in the forests of the night 

As you can see, in just this one line, we have two times, the “tiger” word being used, and with exclamations. The poet is drawing our attention to what we all have seen but never really SEEN, fresh and as if seen for the first time!! 

Here come two words- burning and bright. So, both words together, give us a blinding sense of shine, fire, of the skin of the tiger, and also the word “burning” means passionate, aggressive and powerful. The poet is making us almost SEE the tiger as a NEW VISION!! 

Then you have the words- “IN THE FOREST OF THE NIGHT”. 

What do these words really mean? 

What does “forest OF the NIGHT” mean? 

It means aloneness, and fearlessness and supreme individuality and power. It shows that the tiger is not soft, dependent and needy. It is IN THE FOREST OF THE NIGHT!! 

So much has been conveyed with the powerful first line itself. 

What immortal hand or eye could frame thy fearful symmetry? 

Now the poet is asking, with a fear and wonder, WHICH could make something so beautiful and fearful. He is feeling a great awe at a GOD, or creator, or rather THAT METAPHYSICAL MYSTERY, DREAD AND WONDER, OF who could have the vision to create something so terrible and yet so wonderfully beautiful. 

The poet is now taking his own seeing of a tiger to the highest metaphysical plane of reflection. He is indirectly, deeply and sincerely wondering about and questioning god himself!! 

Who made this tiger? The poet is asking, THIS kind of incredible beast? 

In what distant deeps and skies burnt the fire of thine eyes? 

Here the poet continues, and is asking in which paradise were these eyes made. He is bringing again that feeling of terrible wonder in looking at the tiger. 

On what wings dare he aspire? What the hand dare seize the fire? 

And what shoulder, & what art, Could twist the sinews of thy heart? 

Now the poet is going deeper into wondering about that creator, who made this tiger. What wings, what hand had to catch such a fire, and what shoulder had to make the heart? 

And when thy heart began to beat, 

What dread hand? 

And what dread feet? What the hammer? 

What the chain, in what furnace was thy brain? What the anvil? 

Here the poet is continuing to talk about such a tremendous process of creating the tiger by comparing to furnace. He uses words like hammer, chain, and anvil. 

What dread grasp, dare its deadly terrors clasp! 

Here the poet talks about how a creator could HOLD such a terrifying and powerful beast that is the Tiger. 

When the stars threw down their spears, 

And water’d heaven with their tears, 

Did he smile his work to see? 

Did he who made the Lamb make thee? 

Here the poet is saying that even the stars gave up, with tears, and he continues to ask -did the creator who made the soft lamb, also made the tiger that is such a terrifying and beastly animal? 

Tyger! Tyger! Burning bright in the forests of the night 

What immortal hand or eye dare frame thy fearful symmetry? 

The poet repeats the beginning sentence but adds the word “dare” instead of could. He is gone now to the limit of asking- who created you? Who could dare? Who and HOW did the God make you? 

How could he hold such a power, such a terrifying beast, and how could he make the tiger, while also making the soft and meek lamb? 

Is there no good and bad? Are both the same? And he seems to even admire such a power of a creator to make such a powerful and terriying thing!! 

As we can fully feel this poem, we realize, that Blake is telling us to see reality, see that the tiger is what he is. 

He is conveying with passion and extreme wonder that reality is wild and merciless and that even the creator is merciless!! 

It is a deep wondering, questioning and leaving the answers open, letting YOU see, and think for yourself while giving YOU great eyes to SEE!! 

That is why this poem haunts people who read it. It is one of the greatest poems ever written. 

As we can see, Blake was a romantic but with far deeper questioning of a metaphysical nature. What IS reality? What is good and bad? Is there such a thing? Or is nature just fully what it IS? It is deeply scientific and spiritual at the same time. It is deeply Romantic in the true sense of that word.




*****

THE TYGER BY WILLIAM BLAKE

Tyger Tyger, burning bright, 

In the forests of the night; 

What immortal hand or eye, 

Could frame thy fearful symmetry?


In what distant deeps or skies. 

Burnt the fire of thine eyes?

On what wings dare he aspire?

What the hand, dare seize the fire?


And what shoulder, & what art,

Could twist the sinews of thy heart?

And when thy heart began to beat,

What dread hand? & what dread feet?


What the hammer? what the chain, 

In what furnace was thy brain?

What the anvil? what dread grasp, 

Dare its deadly terrors clasp! 


When the stars threw down their spears 

And water'd heaven with their tears: 

Did he smile his work to see?

Did he who made the Lamb make thee?


Tyger Tyger burning bright, 

In the forests of the night: 

What immortal hand or eye,

Dare frame thy fearful symmetry?