Linear-rotational Analogs - Energy

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.

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