This paper presents a class of bounded continuous time-invariant finite-time stabilizing feedback laws for the double integrator. The authors use Lyapunov theory to prove finite-time convergence. For the rotational double integrator, these controllers are modified to avoid "unwinding." The paper discusses the challenges of designing continuous finite-time-stabilizing feedback controllers due to non-Lipschitzian dynamics. It also addresses the issue of finite-time stabilization for the rotational double integrator, which requires special attention to prevent unwinding. The authors propose a family of continuous time-invariant finite-time-stabilizing feedback laws for the double integrator and a class of globally bounded feedback laws for finite-time stabilization. The results are based on Lyapunov theory for finite-time differential equations. The paper also discusses the rotational double integrator, which has a state space of the two-dimensional cylinder $ S^1 \times \mathbb{R} $, and presents a feedback controller that avoids unwinding. The authors also discuss the non-uniqueness of solutions in non-Lipschitzian systems and the sensitivity of unstable configurations to perturbations. The paper concludes that the non-Lipschitzian nature of the closed-loop system makes the desired configuration globally stable for practical purposes.This paper presents a class of bounded continuous time-invariant finite-time stabilizing feedback laws for the double integrator. The authors use Lyapunov theory to prove finite-time convergence. For the rotational double integrator, these controllers are modified to avoid "unwinding." The paper discusses the challenges of designing continuous finite-time-stabilizing feedback controllers due to non-Lipschitzian dynamics. It also addresses the issue of finite-time stabilization for the rotational double integrator, which requires special attention to prevent unwinding. The authors propose a family of continuous time-invariant finite-time-stabilizing feedback laws for the double integrator and a class of globally bounded feedback laws for finite-time stabilization. The results are based on Lyapunov theory for finite-time differential equations. The paper also discusses the rotational double integrator, which has a state space of the two-dimensional cylinder $ S^1 \times \mathbb{R} $, and presents a feedback controller that avoids unwinding. The authors also discuss the non-uniqueness of solutions in non-Lipschitzian systems and the sensitivity of unstable configurations to perturbations. The paper concludes that the non-Lipschitzian nature of the closed-loop system makes the desired configuration globally stable for practical purposes.