Physics Study Guide/Energy

=Energy=

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 $$(k\Delta\vec{x})\cdot\Delta\vec{x}$$ directly. Since the force actually varies with $$\Delta\vec{x}$$, it is instructive to need a "correction factor" during integration.

Variables

Definition of terms