Energy and Conservation Laws

The Currency of Physics

Energy is a conserved quantity that flows through every physical process, the universal currency of physics. Work is the transfer of energy by a force acting over a distance, measured in joules.

The work–energy theorem states that net work equals the change in kinetic energy. Power is the rate of doing work, $P = \frac{dW}{dt}$, measured in watts.

Conservation Laws

The crown jewel is conservation of energy: in an isolated system with only conservative forces, total mechanical energy $KE + PE$ is constant. Energy converts between forms but is never created or destroyed.

• Free fall: trades potential energy for kinetic energy.
• Friction: converts mechanical energy into heat.
• System bookkeeping: lets you relate initial and final states without tracking detailed motion.

Common pitfall: Confusing energy with power, and forgetting the square in $KE = \tfrac{1}{2}mv^2$. Doubling speed quadruples $KE$, which is why stopping distances grow so sharply.