Physics Study Guide/Energy

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Physics Study Guide (Print Version)
Units Linear Motion Force Momentum Normal Force and Friction Work Energy
Torque & Circular Motion Fluids Fields Gravity Waves Wave overtones Standing Waves Sound
Thermodynamics Electricity Magnetism Optics
Physical Constants Frictional Coefficients Greek Alphabet Logarithms Vectors and Scalars Other Topics

[edit] Energy

Kinetic energy is equal to one-half of mass times the square of velocity.

\mathrm{KE}=\frac{1}{2}m\|\vec{v}\|^2

Kinetic energy is equal to one-half of moment of inertia times the square of angular velocity.

\mathrm{KE}=\frac{1}{2}I\omega^2

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

\mathrm{PE}_g= -m\vec{g}\cdot\vec{x}=mgy

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.

\mathrm{PE}_e=\frac{1}{2}k\|\vec{x}-\vec{x}_e\|^2=\frac{1}{2}k\|\Delta\vec{x}\|^2



Definition of terms

Energy: a theoretically indefinable quantity that describes potential to do work. SI unit for energy is the joule (J). Also common is the calorie (cal).

The joule: defined as the energy needed to push with the force of one newton over the distance of one meter. Equivalent to one newton-meter (N·m) or one watt-second (W·s).

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.

Kinetic energy (K): The energy that an object has due to its motion. Half of velocity squared times mass. Units: joules (J)

Potential energy due to gravity (UG): The energy that an object has stored in it by elevation from a mass, such as raised above the surface of the earth. This energy is released when the object becomes free to move. Mass times height time acceleration due to gravity. Units: joules (J)

Potential energy due to spring compression (UE): Energy stored in spring when it is compressed. Units: joules (J)

Heat energy (Q): Units: joules (J)

Spring compression (Dx): The difference in length between the spring at rest and the spring when stretched or compressed. Units: meters (m)

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•m2)

Angular momentum (ω): Angular velocity times mass (inertia). (rad/s)
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