Energy

Energy ($E$) is the capacity to do Work or cause change. A useful mental model: energy is like a conserved currency that can be stored, transferred, or transformed.

Examples:

• Food stores chemical energy used to move and stay warm.
• A moving car has kinetic energy.
• A raised object stores gravitational Potential energy.
• A lightbulb converts electrical energy into light and heat.

Conservation

In a closed system, total energy is conserved:

$$E_{total}=\text{constant}$$

Energy can move between forms, but it is not created or destroyed. In mechanics, the common forms are kinetic energy and potential energy. If non-conservative effects like friction matter, some mechanical energy becomes thermal energy.

Key mechanical equations

Kinetic energy:

$$K=\frac{1}{2}m{v}^2$$

Work-energy theorem:

$$W_{net}=\Delta K$$

Power is the rate of energy transfer: see Power.

Unit: Joule.

Quick checks

Energy is a scalar, so it does not have direction. But energy transfers can depend on direction because Work uses the component of force along displacement. When solving mechanics problems, first ask whether the system is isolated and whether non-conservative work can be ignored. If yes, conservation of mechanical energy is usually faster than using forces directly.