Past exam of the physics 1 paper of the University of Oxford / 2019 resit / 11 / a

About a fixed origin in an inertial frame, the angular momentum and torque areFor a specified fixed axis with unit vector $\hat{\mathbf{n}}$, use the projections $L_n=\hat{\mathbf{n}}\cdot \mathbf{L}$ and ${\tau }_n=\hat{\mathbf{n}}\cdot \mathbf{\tau }$. The mass is constant. Differentiating and applying Newton's second law,Hence ${\dot{L}}_n={\tau }_n$ for the fixed axis. If the net torque vanishes, the corresponding angular momentum is conserved. Fixing the origin and axis is essential to this unmodified form of the law.