Issac Newton

To Master Index Of Science

  1. Gravity
  2. Newtonian gravity vs General relativity

The Solar System Master.gif

From Here

The Solar System 01


When you compute weight (gravitational mass) of an apple, you know that the earth is pulling it from all over the place. But, you should imagine that it is the center of the earth that is pulling it. This is true when you are computing the gravitational force of any spherical object such as earth – the distance between the center of the earth and the center of the apple shown here is the distance between them.

Mass and Weight

Imagine lifting a 50 kg crate across a smooth floor on earth as shown on the left.

On the Earth the weight of the crate will be 50×10 = 500 N

Gravity changes planet to planet in our solar system.

Now imagine taking the crate to the Moon and lifting it up there. Its mass is still 50 kg but the Moon’s gravitational pull is only about 1/6 of the Earth’s – in other words about 1.6 N/kg. (The Moon has less gravity because it is smaller than the Earth.) This means that the weight of our crate on the Moon will be 50×1.6 = 80 N and so it will be much easier to lift up.

Some examples of other masses are shown in the table.

On other planets the strength of the gravitational field and the acceleration in free fall is different from that on the Earth and so our crate would weigh different amounts if taken to these planets. The table below gives you some weights of our 50 kg crate on other planets.

(Remember that its MASS is the same everywhere including in deep space or in orbit round any planet where it would be weightless!)

Note that larger the planet, more the strength of the gravitational pull on objects towards its center and therefore, more the weight. Jupiter is the largest, therefore, the weight of the 50KG crate is highest there.

It’s interesting to look at the weights of our crate on Earth and on Saturn or Uranus. They are almost the same. That means if you were to go to Saturn or Uranus you would weigh just about the same as you do here. However on Pluto you would be lighter than on the Moon.

What do you think that means about astronauts’ athletic records on Pluto?

Astronauts liked walking on the Moon. They were able to take giant steps because they didn’t weigh as much there. If you were on the Moon you would weigh less than what you do here on the Earth. That is why the astronauts would really like walking on Pluto because they will get a lot lighter because of least gravitational pull, and cover lot more ground compared to other planers with same effort.

On the surface of our Sun the gravity pull is so strong that our crate would weigh an enormous 13 700 N!

Newton’s shell theorem

            • Newton showed that the gravitational effect of a spherically symmetric body is the same as it would be if all its mass were located at its centre (provided that you are outside the body). Planets and stars are nearly spherically symmetric, so one can calculate their gravitational effects using separations from their centres. To prove this requires some mathematics, so we do that in

          this separate file

The Inverse Square Law

inverse squares law

Newtons law of Universal Gravitation.09

Gravitational field strength within the Earth




Free falling Object

See Here for small g

Later in the 1670’s, Newton became very interested in theology. He studied Hebrew scholarship and ancient and modern theologians at great length, and became convinced that Christianity had departed from the original teachings of Christ. He felt unable to accept the current beliefs of the Church of England, which was unfortunate because he was required as a Fellow of Trinity College to take holy orders.

Happily, the Church of England was more flexible than Galileo had found the Catholic Church in these matters, and King Charles II issued a royal decree excusing Newton from the necessity of taking holy orders! Actually, to prevent this being a wide precedent, the decree specified that, in perpetuity, the Lucasian professor need not take holy orders. (The current Lucasian professor is Stephen Hawking.)


Gravitational force acts on all bodies in proportion to their masses. Why, then does not a heavy body fall faster than a light body?

The reason that a heavy body doesn’t fall faster than a light body is because the greater
gravitational force on the heavier body (its weight), acts on a correspondingly greater
mass (inertia).

FHeavy = mHeavy * a
FLight = mLight * a

The ratio of gravitational force to mass is the same for every body – hence
all bodies in free fall accelerate equally. Since  mHeavy mLight ,    FHeavy  has to be heavier than   FLight    so that “a” remains the same for both objects.

And it’s true not just near the Earth, but anywhere.


Master Index of Winter

Back to Season

  1. Shortest day of 2017 — Winter Solstice


Vernal Equinox diagram

On Dec. 21, 2017, or Thursday, the sun will hug the horizon. For those of us in the Northern Hemisphere, it will seem to barely rise — hardly peeking above a city’s skyline or a forest’s snow-covered evergreens — before it swiftly sets.

For months, the orb’s arc across the sky has been slumping, shortening each day.

In New York City, for example, the sun will be in the sky for just over nine hours — roughly six hours less than in June at the summer solstice. The winter solstice marks the shortest day of the year, before the sun reverses course and climbs higher into the sky. (At the same time, places like Australia in the Southern Hemisphere mark the summer solstice, the longest day of the year.)

Today, Jan 21, is the shortest day of 2017 in New Jersey. Here is a picture of sunset at Edison, New Jersey at 4:33 PM.


Michael Faraday

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See Faraday Experiment: From The Wonders of Electricity & Magnetism – Sept 2005 by Prof Walter Lewin [45 to 50 minutes]
Demo of Electric generator [Mins 52:45 to 57:50]

Faraday Experiment Simulator (Click on “5” at bottom right of the simulator)

Michael Faraday, coming from a poor family, received no formal education and worked as an errand boy. In the class-based English society of the time, Faraday had serious trouble fending for himself. After years of hard graft, he got a job of Lab Assistant at Humphry Davy’s Lab at the Royal Institution of Great Britain.

In early part of 1800, magnetism and electricity were two different things. Magnetism meant a strange looking metallic bar that could pull pins, clips, and other metallic stuff towards it. Electricity meant a wire connected to an ugly liquid-filled box called battery. These two “things” were disjointed – there was no connection in between.

In 1831 Faraday demonstrated that when a magnet is moved past a wire, it creates an electric current in the wire. That was the first experiment from where you got electricity not from a battery but from a moving magnet. This opened a new frontier of science and the rest is history. This particular discovery formed the basis of the electricity generator or dynamo that are used today.

Following this discovery, Royal Institution of Great Britain conferred on him the highest honor and made him a fellow. After that ceremony Faraday showed the experimental set up to British PM Robert Peel.

After seeing the demonstration, he asked Faraday ‘But, after all, what use is it?’.

Faraday replied, “I know not, but I wager that one day your government will tax it.”

Faraday’s experiment showed that you can induce current in a closed wire loop by mpving a magnet into it. But that current is feeble and stops as soon as you stop moving the magnet. You cannot do any practical work with that current.

Now, if you want to light a 100 Watt bulb in a Lab, you need to put thouands of loops around a core and then move it manually by rorating it with a handle very fast within a very strong magnet (same as moving magnet towards wire).

Which means that you have to put in energy — here manual — to move the coil to induce meaningful electrical current to light a bulb.

If you want to generate electricity on a big scale you need energy sources such as coal, or oil or nucluer energy.

Light bulbs, TVs  consume energy. This energy consumption is expressed in Watts named after james Watts.

Demo of Electric generator [Mins 52:45 to 57:50]

Note: Albert Einstein kept a picture of Faraday on his study wall at Princeton, alongside pictures of Isaac Newton and James Clerk Maxwell.

Hans Christian Ørsted

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From The Wonders of Electricity & Magnetism – Sept 2005 by Prof Walter Lewin [42 to 45 minutes]

suspended bar magnet

Figure 1. A  compass needle is really a very small magnet. You can make a compass with a bar magnet by hanging it with a piece of paper like this.

north pole of a magnet pointed toward a compass

Figure 2. When a magnet is pointed to the compass needle, the needle moves.

Image result for oersted experiment


Figure 3. Oerstead achieved the same result by replacing the bar magnet of Figure 2 with a piece of wire connected to a battery. This proves that an electric circuit behaves the same way to a compass as a bar magnet does.

Stick your thumb out on your right hand, and imagine holding the wire with your thumb pointing in the direction that current is flowing (opposite to electron flow). As your fingers curl around the wire, so are the magnetic field lines circling the conductor.

experiment to show effect of an electromagnet on a compass


Oersted experimented with  a compass, which has magnetic poles to show you which direction you are facing.

He had put the compass over a closed current loop connected to a DC battery. Then, by using a switch, he turned the circuit ON and OFF.

As soon as he turned the switch ON from the OFF state, the currect went through the wire and he was able to cause the compass needle to move.

As soon as he turned off the switch, the compas needles went back to their original position.

So he was able to demonstrate that the magnet responds to the flow of current.

He concluded that when the current was going throu ght wire, the wire became magnetic. The physicists would say the the current creates a magnetic field.

In other words, moving electric charges or electrons, creates a magnetic field. That is what Oersted showed.

Now comes the key question:

If moving electrons can create a magnetic field, can a moving magnet create an electric current?

The answer was given by Michael Faraday in 1831. The answer is Yes.  The demo of faraday’s experiment is given during the 46th to 50th minute of the lecture.

When Faraday made this discovery, a reporter asked him if this discovery will be of any practical use? Faraday answered: Some day you will tax it.

From Manual Power To Electricity

Back to Industrial Revolution

The Cotton Manufacture to Modern factory

Gauss’s Law

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8.02x – Lect 3 – Electric Flux, Gauss’ Law, Examples By Prof. Walter Lewin, MIT

Gauss’s Law

Gauss Law Diagram 05

a. Within a charged metal sphere, the electric field E=0
b. Outside a charged metal sphere, the magnitude of the electric field E decreases with the square of the radial distance from the center of the sphere

E = (1⁄4πε0)q/r2

Gauss Law Diagram 03

Note that electric field always move outward from a positive charge and into a negative charge.

Gauss Law Diagram 07

q2 is positively charged because the lines of electric field emerge from it. Consequestly, q1 is negative.

In order to find the  capacitance of this capacitor, you need to understand Gauss’s Law.

Gauss Law Diagram 06


Gauss Law Diagram 08

Figure 6.3. Illustrations of spherically symmetrical and nonsymmetrical systems. Different shadings indicate different charge densities. Charges on spherically shaped objects do not necessarily mean the charges are distributed with spherical symmetry. The spherical symmetry occurs only when the charge density does not depend on the direction. In (a), charges are distributed uniformly in a sphere. In (b), the upper half of the sphere has a different charge density from the lower half; therefore, (b) does not have spherical symmetry. In (c), the charges are in spherical shells of different charge densities, which means that charge density is only a function of the radial distance from the center; therefore, the system has spherical symmetry.

1. Concept of Electric flux

2. Concept of Spherical Symmetry [Ref 1], Ref 2]

  • A spherical shell with uniform charge density creates no electric field inside itself.

3. A golf ball is moved when it is being hit by a club.
When two positive charges are placed side by side, they move away like somebody is hitting them. Where does this force that moves the charges away come from. Its called the electric force.

4. Gauss and Coulomb’s law are in a way the same law. They both link the electric field with the charge Q.
Key is that the electric force falls off as one over R square.
If the electric firld did not fall off as one over R squared, Gauss’s law would not even hold.

Gravitational forces also fall of as one over R squared.

Therefore if you take a hollow spherical planet, it means that there would be no gravitational
force inside that hollow planet. So if you were there there would be no gravitational force
on you.

But if it were a cubical planet then the gravitational field inside would not be zero. Newton intuitively senses that it was
correct that if you have a planet with uniform mass distribution, then you can consider it a point mass
as long as you are outside the planet.

But it took him 20 years to prove it and he finally published his results. [23:09]

This is spherical symmetry number one.

Demonstration of Gauss’s Law by using Van de Graaff [ starts from 34:30 Minute ]

Instrument Wimshurst

Instruction 5.1.4 Applet to demonstrate the fields generated by various charges.



Coulombs Law

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Electrostatics is a branch of physics that deals with study of the electric charges at rest.

Since classical physics, it has been known that some materials such as amber attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word ‘electricity’. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb’s law. Even though electrostatically induced forces seem to be rather weak, they are much higher than Newton’s gravitational forces. For example, electrostatic forces between an electron and a proton of a hydrogen atom is about 36 orders of magnitude stronger than the gravitational force acting between them.

Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static ‘shock’ is caused by the neutralization of charge built up in the body from contact with insulated surfaces.

Before the year 1832, when Michael Faraday published the results of his experiment on the identity of electricities, physicists thought “static electricity” was somehow different from other electrical charges. Michael Faraday proved that the electricity induced from the magnet, voltaic electricity produced by a battery, and static electricity are all the same.

Charles-Augustin de Coulomb 14 June 1736 – 23 August 1806

Inverse square law for electrically charged bodies
Coulomb discovered the relationship between the force that exists between two electrically charged bodies — e.g.  glass rods rubbed with the silk — and the distance that separates them, known as Coulomb’s Law.
He showed that the electrical force between charged bodies varies inversely as the square of the distance between them, and is porportional to the charge of each, being an attractive force for opposite charges, and a repelling force for charges of the same kind.

A body in this example could be a glass rod rubbed with the silk to produce a negative chargeor a rubber rod with cat fur to produce a positive charge. (When you rub a rubber or plastic  rod with fur, the plastic rod becomes negatively charged and the fur becomes positively charged.)

The concept is very similar to Newton’s Third Law. But Newton deals with masses of physical objects (m1, m2 etc) while Coulomb deals with electric charges residing within physical bodies such as glass or plastic rod etc.

Coulombs Law
Image result for coulomb

Newton’s Third Law


Coulomb’s Law

Image result for coulombic attraction

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1. Baloons and Static Electricity — Simulation

Two rubber balloons can be suspended from the ceiling  at approximately head height. When rubbed upon a teacher’s head, the balloons became charged as electrons are transferred from the teacher’s fur to the balloons. Since the teacher’s fur lost electrons, it becomes positively charged and the baloons becomes negatively chrged. When the teacher pulls away from the balloons, the balloons experienced a repulsive interaction for each other since both are negative. Now, when the teacher draws their head close to one baloon, the baloon sticks to the head since they are oppositely charged.

File:Ampere coulomb.svgNext

Electroscope: used to detect the presence and magnitude of electric charge on a body.

What happens when a rubber rod is rubbed with cat’s fur?

How Charging by Friction Works
The frictional charging process results in a transfer of electrons between the two objects that are rubbed together. Rubber has a much greater attraction for electrons than animal fur. As a result, the atoms of rubber pull electrons from the atoms of animal fur, leaving both objects with an imbalance of charge. The rubber  has an excess of electrons and the animal fur has a shortage of electrons. Having an excess of electrons, the rubber stick is charged negatively. Similarly, the shortage of electrons on the animal fur leaves it with a positive charge. The two objects have become charged with opposite types of charges as a result of the transfer of electrons from the least electron-loving material to the most electron-loving material.


  1. Coulomb’s Law — Like charges repel, unlike charges attract
  2. Electric Charges: “Coulomb’s Law” 1959 PSSC; Eric Rogers; Princeton University

  3. 8.02x – Lect 1 – Electric Charges and Forces – Coulomb’s Law – Polarization by Walter Lewin MIT
    1. See the comparison between Coulomb’s law between electric charges and Newton’s Third Law on masses from 38:00 onwards
    2. Notice how the force between electric charges is so much more higher than the force between masses (Electric force Vs Gravitational force)
    3. Review Newton’s Third Law 
    4. Exercise

Engines, Electricity, Evolution

Back to The Industrial Revolution

    1. Engines
      1. Internal Combustion Engine
    2. Electricity
      1. Induction motors
      2. Alternator
      3. Inverters

The Internal Combustion Engine


  • An ICE is a completely mechanical device. Hence the name “engine”, whereas, “motor” denotes an electrical device.

Four steps of a 4-cylinder ICE:

  1. Intake
  2. Combustion
  3. Power
  4. Exhaust
    • Intake: As the piston moves downwards, the intake valve opens to fill fuel and air in the combustion chamber.
    • Combustion: Next the intake valve closes and the piston moves upwards that compresses the fuel and air mixture.
    • Power: Next the spark plug ignites the compressed fuel and air mixture causing it to burn explosively which forces the piston into another downward stroke.
    • Exhaust: As the piston begins its second upwards stroke, the exhaust valve opens and the burned air fuel mixture is forced out of the combustion chamber.

Cooling System Parts
1. Water pump: Heart of cooling system which pumps the coolant
2. Radiator
3. Thermostat
4. Coolant Temperature Sensor (CTS)
5. Coolant (Antifreeze + water)

How an engine works – comprehensive tutorial animation featuring Toyota engine

Induction Motors

  1. How does an Induction Motor work ? By Learn Engineering


  1. They generate AC power at a specified frequency – they are the workhorse of the power generation (PSE&G) industry
  2. The magnetic poles on the rotor  are powered by DC Generator
  3. Electricity is produced by ELectro-magnetic induction. Here a magnetic field rotates with respect to a coil
  4. Rotor produces rotating magnetic flux which induces electricity in stationary armature coils

From:  How does an Alternator work ? By Learn Engineering


  1. Inverters, How do they work? By Learn Engineering