This section discusses energy and power in rotating mechanical systems. It is assumed you already know about energy and power in translating mechanical systems. Accordingly, this page is rather brief.

The potential energy, U, stored in a rotational spring with spring constant K_{r}
that is wound to an angle θ is

(*Translating system equivalent:*
)

The kinetic energy, T, stored in a rotating mass with moment of inertia J and angular velocity ω is

(*Translating system equivalent:*
)

Dissipated energy in a friction element, B_{r}, with angular
velocity, ω, is given by

(*Translating system equivalent:*
)

Power in rotating systems is given by

(*Translating system equivalent:*
)

where τ is the torque and ω is the angular velocity.

Note: the previous page showed that power is conserved when there are gears in the system, but there is a tradeoff between angular velocity and torque.

© Copyright 2005 to 2019 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College