# Energy and Power in Rotating Mechanical Systems

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.

## ENERGY

### Potential Energy

The potential energy, U, stored in a rotational spring with spring constant Kr that is wound to an angle θ is

(Translating system equivalent: )

### Kinetic energy

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

(Translating system equivalent: )

### Dissipated Energy

Dissipated energy in a friction element, Br, with angular velocity, ω,  is given by

(Translating system equivalent: )

## POWER

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.

References