Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 32_E

A particle is acted on by two torques about the origin: \(\vec{\tau}_1\) has a magnitude of \(2.0 \text{ N}\cdot\text{m}\) and is directed in the positive direction of the \(x\) axis, and \(\vec{\tau}_2\) has a magnitude of \(4.0 \text{ N}\cdot\text{m}\) and is directed in the negative direction of the \(y\) axis. In unit-vector notation, find \(d\vec{\ell}/dt\), where \(\vec{\ell}\) is the angular momentum of the particle about the origin.