Linear-rotational Analogs - Energy


The mechanical work done by an external agent on a system is equal to the change in kinetic energy of the system:

General work-energy theorem (translation and rotation)

The work done W by an external agent which exerts a force F (at r) and torque τ on an object along a curved path C is:

where θ is the angle of rotation about an axis defined by a unit vector n.

Kinetic energy
Elastic potential energy

For a stretched spring fixed at one end obeying Hooke's law:

where r2 and r1 are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.

Read more about this topic:  Linear-rotational Analogs

Famous quotes containing the word energy:

    The principle of avoiding the unnecessary expenditure of energy has enabled the species to survive in a world full of stimuli; but it prevents the survival of the aristocracy.
    Rebecca West (1892–1983)

    The persons who constitute the natural aristocracy, are not found in the actual aristocracy, or, only on its edge; as the chemical energy of the spectrum is found to be greatest just outside of the spectrum.
    Ralph Waldo Emerson (1803–1882)

    The flattering, if arbitrary, label, First Lady of the Theatre, takes its toll. The demands are great, not only in energy but eventually in dramatic focus. It is difficult, if not impossible, for a star to occupy an inch of space without bursting seams, cramping everyone else’s style and unbalancing a play. No matter how self-effacing a famous player may be, he makes an entrance as a casual neighbor and the audience interest shifts to the house next door.
    Helen Hayes (1900–1993)