often used in computer printers, optical scanners, and digital photocopiers to move the active element, the print head carriage (inkjet printers), and the platen or feed rollers. So-called quartz analog wristwatches contain the smallest commonplace stepping motors; they have one coil, draw little power, and have a permanent magnet rotor. The same kind of motor drives battery-powered quartz clocks. Some of these watches, such as chronographs, contain more than one stepper motor. Closely related in design to three-phase AC synchronous motors, stepper motors and SRMs are classified as variable reluctance motor type. Linear motor A linear motor is essentially any electric motor that has been "unrolled" so that, instead of producing torque (rotation), it produces a straight-line force along its length. Linear motors are most commonly induction motors or stepper motors. Linear motors are commonly found in roller-coasters where the rapid motion of the motorless railcar is controlled by the rail. They are also used in maglev trains, where the train "flies" over the ground. On a smaller scale, the 1978 era HP 7225A pen plotter used two linear stepper motors to move the pen along the X and Y axes. Comparison by major categories Electromagnetism Force and torque An electric motor converts electrical energy to mechanical energy through the force between two opposed magnetic fields. At least one of the two magnetic fields must be created by an electromagnet through the magnetic field caused by an electrical current. The force between a current in a conductor of length perpendicular to a magnetic field may be calculated using the Lorentz force law: Note: X denotes vector cross product. The most general approaches to calculating the forces in motors use tensor notation. Power Where is shaft speed in rpm and T is torque, a motor's mechanical power output Pem is given by, in Imperial units with T expressed in foot-pounds, (horsepower), and, in SI units with shaft angular speed, , expressed in radians per second, and T expressed in newton-meters, (watts). For a linear motor, with force F expressed in newtons and velocity v expressed in meters per second, (watts). In an asynchronous or induction motor, the relationship between motor speed and air gap power is given by the following: , where Rr – rotor resistance Ir2 – square of current induced in the rotor s – motor slip; i.e., difference between synchronous speed and slip speed, which provides the relative