Rotational work

Definition

Rotational work is the work done by a torque in causing an object to rotate about a fixed axis. It is calculated as the product of the torque and the angular displacement of the object.

5 Must Know Facts For Your Next Test

1. Rotational work ($W$) is given by $W = \tau \theta$, where $\tau$ is the torque and $\theta$ is the angular displacement in radians.
2. The unit for rotational work in the SI system is the joule (J).
3. Positive rotational work indicates that the torque is acting in the direction of rotation, while negative rotational work indicates it is acting against it.
4. If there is no angular displacement ($\theta = 0$), no rotational work is done regardless of the amount of torque applied.
5. Rotational work can be linked to kinetic energy through the equation $W = \Delta K_{rot}$, where $\Delta K_{rot}$ represents a change in rotational kinetic energy.

Review Questions

• What are the units used to measure rotational work?
• How do you calculate rotational work when given torque and angular displacement?
• Explain what happens to rotational work if there is no angular displacement.

Related terms

Torque: A measure of how much a force acting on an object causes that object to rotate. It is calculated as force multiplied by lever arm distance.

Angular Displacement: The angle through which an object moves on a circular path. It is measured in radians.

Rotational Kinetic Energy: The energy possessed by a rotating object due to its motion, given by $K_{rot} = \frac{1}{2} I \omega^2$, where $I$ is moment of inertia and $\omega$ is angular velocity.