6.3 Kinetic energy
The energy associated with motion is called kinetic energy. Since there are two kinds of motion (translational and rotational), there are two kinds of kinetic energy.
6.3.1 Translational kinetic energy
For an object with a mass m, traveling in a straight line with a speed v (we generally drop the absolute value signs for convenience when working with energy), the kinetic energy is given by the expression
K = 1⁄2mv2
From this expression, we see how to express the joule in base SI units: 1 J = 1 kg · m/s2
Remember, speed is the magnitude of velocity. This means energy is a scalar quantity. Kinetic energy is not associated with any particular direction of motion,* only how fast the object is going.
Practice
6.3.2 Rotational kinetic energy
The following table lists the moment of inertia of several common objects. The column labeled “type of motion” is a sort of generalization, to describe how the object is rotating. For example, if the type of motion is “rolling,” visualize the object spinning around a central axis as if it were wheel. An object rotating like this may be spinning in place, or rolling forward, but the moment of inertia would be the same–the moment of inertia depends on the shape of the object and its axis of rotation.
For a specific example, a disk (which is simply a very short cylinder) that is rolling forward would have the same moment of inertia as a disk that is acting as a pulley and rotating in place. However, if the disk is flipping end-over-end, like you would flip a coin, the moment of inertia would be different.
Practice
In this problem you’ll need to consider how an object’s mass distribution affects its moment of inertia.
*This is one of the limitations of energy analysis. Just like any tool, it is not necessarily the best for every situation.