# Rotational Work

on . Posted in Classical Mechanics

Rotational work, abbreviated as $$W_r$$, also known as torque work, is the work done when torque is applied to an object and causes it to rotate around a fixed axis.  Torque is the measure of the tendency of a force to cause an object to rotate about an axis and is often applied to objects with rotational motion, such as wheels, gears, and flywheels.  When a torque is applied to an object and it undergoes rotational motion, work is done to transfer energy to the object, allowing it to rotate.

The angular displacement is measured in radians because angular quantities are often expressed in radians rather than degrees in the context of rotational motion.  One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

If the torque and the angular displacement are in the same direction (both causing the same sense of rotation), the work done is positive.  If they are in opposite directions (resisting the rotation), the work done is negative.  Rotational work can be used to calculate the energy transferred to a rotating object or the energy required to make an object rotate.  It's an important concept in mechanics and engineering, particularly in the design of machines and systems involving rotational motion.

### Rotational Work formula

$$W_r = \tau \; \theta$$     (Rotational Work)

$$\tau = W_r \;/\; \theta$$

$$\theta = W_r \;/\; \tau$$

Symbol English Metric
$$\large{ W_r }$$ = rotational work $$\large{lbf - ft}$$ $$\large{J}$$
$$\large{ \tau }$$  (Greek symbol tau) = rotational force $$\large{lbf-ft}$$ $$\large{N-m}$$
$$\large{ \theta }$$  (Greek symbol theta) = angular position $$\large{deg}$$ $$\large{rad}$$

Tags: Torque