Pies and circles

Dear Samarth,

I have always told you that there are two Pies in a circle. 

Actually, there is a greek alphabet pi, which is what we talk about when we say pie when we are talking about a circle.  Here's how it looks:

The circle is very interesting geometrical shape. There is a single thing that describes a circle: its "radius". If you gave someone the radius of a circle you have, that person can draw exact same size circle using that radius. 

You know what an angle is right? We measure the angle in units of degrees or radians. A circle has 360 degrees, but there is an interesting way of measuring the angle in radians. A "radian" is a measured differently:

If you walked around the circle on its edge, a distance that is the same size as the "radius" of the circle, the angle spanned by you is exactly equal to 1 radian. So how many "radians" are there in a circle. Exactly "2 pi" radians. 

Hence, we say that there are 2 pies in a circle. Now you know the real secret.

Love, 

Papa

 

Vectors

Dear Samarth,
Do you remember the picture I showed about an air-plane which was flying at an angle although it wanted to go straight because there was a wind pushing it?

What about the life saver that was dropped from the air-plane, how it was moving both forward at the same time it was going down?

Vectors helps up with breaking such problems into easy pieces. So for example, we break speed into vertical speed and horizontal speed and then it becomes easy for us to find things like how much distance the air-plane covered in 10 seconds and how far the life saver dropped in 10 seconds. For horizontal distance if we know that air-plane travels 100 meters in 1 second then it will travel 1000 meters in 10 seconds. Right?

We do the same for vertical and say in 10 seconds it drops 500 meters. Then we know where the life saver will drop in 10 seconds.

See the picture below:

Let's say a car is moving in the direction of the line marked with SPEED. We break the vertical speed as VSPEED and horizontal speed as HSPEED. So we can say the speed of the car is

HSPEED*x + VSPEED*y

It is the sum of vertical and horizontal speed. The car is actually moving along SPEED, which is sum of speed in x-direction and speed in y-direction. Does that make sense?

A vector in essence has both speed and direction. When you add two vectors, you add the individual direction together, but you can't add the x-direction variable with y-direction variable.

Here's a small problem. Can you tell which boat will reach the other shore first?

Love
Papa

Michael Faraday and electromagnetic field theory

Dear Samarth,
Remember the story of Michael Faraday I told you last night. He pioneered the field of electromagnetism. He studied electricity and magnetism. It is largely because of his effort that electricity becomes available for use in technology.

All motor, generators and transformers are based on the electro-magnetic principles that he discovered. Electromagnetism means that changing magnetic field field produces electric current.

Faraday proposed that electromagnetic forces extended into the empty space around the conductor. Nobody believed him at first and it was established only after his death. He came up with ideas about how to think and visualize the electromagnetic fields. Here's how the fields look like around the magnet:

It is easy to draw magnetic fields using compass. We did that as science experiment in schools. See the picture below:

We can do it at home if you like.

Michael Faraday was a great scientist who invented many other things. You can read more about him here.

Love,
Papa

What is a real transformer?

Dear Samarth,
I know you love transformer cars, but you wanted to know what is a real transformer, right?

Do you know that we can create electricity using magnets? When you pass electricity through a coil, then you create an invisible magnet. See the image below:

The image shows what happens when current is passed through the coil. The lines and arrows show the magnetic fields. The more turns that we add and the higher the current through the coil, the stronger is the invisible magnetic field. If we put iron rod inside this coil, the invisible magnetic field will convert this iron into a magnet. See this picture:

Similarly you can create current, when you pass a magnet through a coil. That's what we do in hydro-electric power plants and dynamos in cars (did you notice we never change batteries in real cars).

You create a transformer when you have two coils in an iron core one with more turns and other with less turns. When you pass current through one of the coils, the magnet generates current in the other coil. The following picture shows this:

Real simple right?

Love,
Papa

About Holi

Dear Samarth,

This email I want to tell you about Holi. Holi is a festival of colors. People use either wet colors or dry colors on each others. 

When I was young it was a great festival for us to come together. All kids would go out and play colors in the early morning, then all uncles would go out around 11:00 am to play Holi and later ladies would go out. Each family would prepare lots of snacks, so later when everyone was tired, they would go sit in someone's garden and would get helpings of snacks. It was normal for 100-500 people to turn up at your house on the day of Holi. Later after the snacking people would go home and try to get the color off their face and hands. Most time it would not go out completely. 

 

Later in the evening people would wear new cloths and again go around to everyone home for wishing well to everyone. Irrespective of big and small people would give hugs to each other. Later we would gather in our local temple and we would have Bhajans and songs. In India we still celebrate the festival of Holi with lots of festivities. 

Holi actually starts a day before with a bonfire on the full moon night. We would collect dry twigs and branches to make a bonfire. Several of the people would do fire tricks. We used to do it near a pond in our colony. Holi is celebrated at a time when the weather is just a wee bit cold so gathering around a fire is fun.

So why do we celebrate Holi? You remember the story of Prahlad. 

The bonfires are lit in memory of the miraculous escape of Prahlad when Demoness Holika, sister of Hiranyakashipu, carried him into the fire. Holika was burnt but nothing happened to Prahlad. Lord Vishnu comes out of pillar in his Narasimha avatar to protect Prahlad and kill Hiranyakashyapu. In ways, it symbolizes that Lord is present everywhere and no-one is more powerful than him. 

Lord Krishna popularized the festival of Holi by playing pranks on the gopis when he was a kid. 

And that's why mamma has made gujiya for all of us to enjoy on Holi. 

Love

Papa

Fulcrum

Samarth,
I want to tell you about Fulcrum in this email.

You remember the stories about Archimedes "Eureka". How he ran naked on the streets of Rome. The same Archimedes once said: "Give me a place to stand and with a lever I will move the whole world." Amazing, isn't it. Archimedes was a brilliant scientist.  The earth is so heavy and yet he thought that he could move it. But how? Was he serious when he said that?

Yes he was serious, and yes even you can move a really heavy object like a really huge boulder. 10 or even 100 times heavier than yourself. Here's how it works. You have been on seesaw right? 

See the small guy he really can lift the big guy, but only if the length of the seesaw on his side is large enough to counter weigh the weight of the fat guy. See this picture below. 

The small ball is able to lift the big ball because the length of the seesaw on its end of seesaw is larger compared to the seesaw length on the side of the big ball. So if the length of lever on your side of seesaw is 10 times the length on the other side, you can lift 10 times your weight. If it is 100 time you will be able to lift 100 times your weight. 

Your weight is around 25 Kilograms. Do you know what is the weight of earth?  How long of a lever you will need?

The middle triangular shaped object is called Fulcrum.

Love,

Papa