Basic Rotational Mechanics

Force and Mass

In linear mechanics, the relationship between force and acceleration is given by Newton's Second Law of Motion:

Force = Mass * Acceleration

Under constant velocity, there is no acceleration and the sum of the forces is zero.

In rotational dynamics, this is given by:

Torque = mass moment of inertia * angular acceleration

Torque is the force operating in a circular rotation.

Mass moment of inertia = resistance of a mass to a change in rotation direction (also called angular momentum).

If a system is rotating at constant speed, the sum of torques will be zero.

Define positive rotation as the counter clockwise direction. Then positive torque is counter-clockwise and negative torque is clockwise.

If an electric motor drives a load of 10Nm, then at steady state there is a 10Nm mechanical torque (rotational force) that is opposing the rotation (clockwise, or negative).

There must be an equal and opposite positve (counter clockwise) torque produced by the motor.

In a generator, an external mechanical system drives rotation, therefore the mechanical torque from the driving system will be in the direction of motion (positive, counter-clockwise) and in steady state the electrical machine will produce an equal and opposite torque (negative, clockwise).

When a motor is not operating in steady state it creates a torque with a magnitude that is not equal than the load:

motor torque − load torque = mass moment of inertia

If motor torque is greater than load torque, the motor will accelerate.

If load torque is greater than motor torque, the motor will decelerate.

A motor produces torque that supports the motion

A generator produces torque that opposes the motion

Mechanical Power

Work = force * distance = torque * rotation circumference

Mechanical power = work per unit of time

Mechanical power = torque * rotations per unit of time

Mechanical power = torque * rotating speed