# Physics Study Guide/Energy

# Energy[edit]

Kinetic energy is simply the capacity to do work by virtue of motion.

**(Translational) kinetic energy** is equal to one-half of **mass** times the square of **velocity**.

**(Rotational) kinetic energy** is equal to one-half of **moment of inertia** times the square of **angular velocity**.

**Total kinetic energy** is simply the sum of the translational and rotational kinetic energies. In most cases, these energies are separately dealt with. It is easy to remember the rotational kinetic energy if you think of the moment of inertia I as the *rotational mass*. However, you should note that this substitution is not universal but rather a rule of thumb.

Potential energy is simply the capacity to do work by virtue of position (or arrangement) relative to some zero-energy reference position (or arrangement).

**Potential energy** due to gravity is equal to the product of **mass**, **acceleration** due to gravity, and **height (elevation)** of the object.

Note that this is simply the vertical displacement multiplied by the weight of the object. The reference position is usually the level ground but the initial position like the rooftop or treetop can also be used. **Potential energy** due to spring deformation is equal to one-half the product of the **spring constant** times the square of the **change in length** of the spring.

The reference point of spring deformation is normally when the spring is "relaxed," i.e. the net force exerted by the spring is zero. It will be easy to remember that the one-half factor is inserted to compensate for finite '"change in length" since one would want to think of the product of force and change in length directly. Since the force actually varies with , it is instructive to need a "correction factor" during integration.

## Variables

g: local acceleration due to gravity (on the earth’s surface, 9.8 m/s^{2})h: height of elevation (m)U Potential energy (J)_{e}:k: spring constant (N/m)Δx: change in length of spring (m) |

## Definition of terms

**1 joule = 1 J = 1 newton • 1 meter = 1 watt • 1 second**
Energy comes in many varieties, including Kinetic energy, Potential energy, and Heat energy. Potential energy due to spring compression (U Energy stored in spring when it is compressed. Units: joules (J)_{E}):Heat energy (Q): Units: joules (J)Spring compression (D The difference in length between the spring at rest and the spring when stretched or compressed. Units: meters (m)_{x}):Spring constant (k): a constant specific to each spring, which describes its “springiness”, or how much work is needed to compress the spring. Units: newtons per meter (N/m)Change in spring length (Δx): The distance between the at-rest length of the spring minus the compressed or extended length of the spring. Units: meters (m)Moment of inertia (I): Describes mass and its distribution. (kg•m^{2})Angular momentum (ω): Angular velocity times mass (inertia). (rad/s) |