The work done by a constant torque is calculated by multiplying the torque by the angular displacement: $W = \tau \Delta \theta$.

The work done by a variable torque is calculated by integrating the torque with respect to the angular displacement: $W=\int_{\theta_{1}}^{\theta_{2}} \tau d \theta$.

The work done is equal to the area under the torque vs. angular position curve.

Identify all the torques acting on the object and their respective angular displacements.

Apply the work-energy theorem or the principle of conservation of energy to relate the work done to the change in rotational kinetic energy.

Torque is a rotational force that can transfer energy to or from an object when applied over an angular displacement.

Angular displacement is the angle through which an object rotates.

Work in rotational motion is the energy transferred by a torque acting over an angular displacement.

Moment of inertia is a measure of an object's resistance to changes in its rotational motion.

Rotational kinetic energy is the kinetic energy due to the rotation of an object and is given by $\frac{1}{2}I\omega^2$, where I is the moment of inertia and $\omega$ is the angular velocity.

Energy is transferred into the system, increasing its rotational kinetic energy.

Energy is transferred out of the system, decreasing its rotational kinetic energy.

The work done is doubled.

The work done is doubled.