Rederive

Preamble

If matter is the bread of physics, energy is the butter (actually, it would be more appropriate to say energy is BOTH the bread AND the butter, and mass is a very processed bread).

What is energy? Again intuitively, the concept of energy is engraved in everyone’s brain. From sci-fi movies where you see laser beams and explosions, to fantasy films with wizards throwing fireballs, you surely have a good way of imagining energy. Now, you need to learn how to imagine that energy moving from one object to another.

Types of Energy

Before talking about energy as one, let us first overview some common manifestations of energy.

Firstly of course, we have Kinetic energy. We denote it by K. When an object moves, it gains velocity and momentum. We say that this body has energy due to its motion. It is this energy that gets drained from friction and causes the object to slow down. When you push a desk, it moves forward and slows down until it stops. This all happens very quickly due to the frictional forces; however, it seems like the ground is sapping strength from the desk. This ‘strength’ is the energy of the body, which is used up in dragging against the ground.

TL: DR, when a body moves it has kinetic energy.

A body can move straight (called translational motion), in circles (angular motions), or it can move to-and-fro or oscillate (called vibrational or oscillatory motion). Each of these has a specific amount of energy contributing to them, respectively called translational kinetic energy, angular/orbital kinetic energy, and vibrational kinetic energy.

A body possesses some energy due to its shape and size too. This is called Potential energy. Although potential energy is a rich concept in itself, I shall explain the basics here. Sometimes, the laws of physics in a system say that an object should behave in a certain way. For example, Law of Gravitation says that due to the Earth’s gravitational field, things should always fall. This is why you come back down when you jump. Now imagine you’re trying to hang on from a bar (dead hangs are a great way to learn how to do pull-ups by the way). It suddenly gets hard, right? Jumping was easy but staying up is so difficult!

Your body tends to fall due to gravity. Now, you’re physically making it stay up by hanging from the rod. In essence, you are storing some energy in your body that makes it resist the act of falling. You get tired because you need to be doing this continuously and your muscles reach their limit. But as long as you’re hanging, you have Gravitational Potential Energy. Same logic applies to stretching a rubber band till it gets hard (imagine it!).

The energy possessed by current in circuits is called Electric energy.

In compounds, atoms are bonded together (look in chemistry). These bonds have a certain energy stored in them, called Chemical energy.

When energy moves from one body to another, temperature can change. Energy is called Thermal energy or simply Heat when it moves between bodies and is associated with the body’s temperature.

From Here On…

You must realize that there is no distinction between energy. All these types discussed are the same phenomenon, being manifested in different ways. This is very important because later on you will deal with interconversions of these energies.

As for mass, it is equally as important. For a lot of physics and chemistry, we deal with the Law Of Conservation Of Mass. This law says that in any physical or chemical change (emphasis on these two only!), the total mass of the system will remain constant. This is pretty obvious for everyone, since you could have been using this assumption throughout your life for everything.

For now, just consider your bread to be mass, and your butter to be energy. Even with a more processed bread, you could still make a pretty good toast!