Definition 14.2.1. Rotational Work.
The work done by a torque \(\vec{\tau}\) on an object rotating through \(\vec{d\theta}\) is:
\begin{equation*}
W = \int_{\theta_i}^{\theta_f} {\vec{\tau} \cdot \vec{d\theta}}
\end{equation*}
Section 14.2 Rotational Work
Since there is kinetic energy associated with rotation, it stands to reason that energy can be transferred into or out of a system via a rotational interaction. In fact, you can create an angular analogue for Work
As with work done by a force, if the torque is constant you can simply write
\begin{equation*}
W = \vec{\tau} \cdot \vec{\Delta \theta}
\end{equation*}
Importantly, this work is in addition to any work done by the forces acting on the system.
Exercises Activities
1. Calculation: Unwinding a Spool.
Suppose you unwind a string that has been wrapped around a spool of radius \(R\) three times, causing the spool to gain a known amount of rotational kinetic energy \(K_{rot}\text{.}\) Find the magnitude of the force you exerted on the string.
