In addition to forces and accelerations, energy is an alternative tool we can use to understand how systems behave. We will spend a lot of time on energy, and the closely related idea of electric potential, in EMP-Cubed. This page contains brief reminders of the key ideas about energy from your mechanics course; for more details refer to the readings from Physics 183.

It's actually not easy to give a precise definition of energy that covers all of the situations in which it occurs. For our course, a reasonable way to think about it is that energy is either motion, or the ability to produce motion. (However, some forms of this motion, like random molecular motion associated with thermal energy produced by friction, may be difficult to see.)

There are two important types of energy we talk about: kinetic energy, which is the energy associated with objects currently moving in a particular direction, and potential energy, which is energy stored somehow in a system that could cause things to move in the future (like a compressed spring that could push a block and make it move).

A really nice feature of energy is that energy is a scalar, not a vector. Energy is just a number without any direction associated with it, which means there are no x and y components and no trigonometry to worry about.

Several symbols are commonly used to represent energy. $E$ is the most common symbol representing any kind of energy. If we want to remind ourselves that the energy is kinetic energy, we often use $K$, and $U$ is generally used to represent potential energy (sometimes with a subscript to specify what kind of potential energy, like $U_g$ for gravitational potential energy). Regardless of the type of energy, the SI unit of energy is the joule (J), which is equivalent to 1 kg m²/s². Using the definition of a newton, you can also write this as 1 J = 1 N m.

An alternative (non-SI) unit of energy that may be more convenient in this course is the electron-volt, eV, which has a value of 1 eV = $1.602 \times 10^{-19}$ J.

Energy is important because energy is a conserved quantity – energy is never created or destroyed, it only changes form, for example from $K \rightarrow U$. This means that for any isolated system, if you compare two snapshots of the system at different times, the total amount of energy in the system has to be the same. (If your system interacts with its environment, you just need to keep track the energy flowing into or out of the system to make the accounting work out.)

Often, this means that you can figure out the state of the system at some final $t_f$ based on what you know about some initial time $t_i$, without having to calculate anything about what happened in between.