How do I prove whether a force perpendicular to the motion is conservative and $\mathbf{F}=\mathbf{F_{0}}\sin(at)$ conservative, where $\mathbf{F_{0}}$ is a constant vector.
I knew that for a force to be conservative, it's $\nabla \times \mathbf{F}=0$ everywhere or the work done around a closed path without including origin should be zero.
Self-learning from Kleppner and Kolenkow's book.