A pendulum consists of a mass m attached to a string of length L. The pendulum is released from rest at an angle θ from the vertical. What is the speed of the mass at the lowest point of its swing?

Core Concept

At the release point, the pendulum has gravitational potential energy PE = mgh, where h is the height above the lowest point. From geometry, h = L - Lcosθ = L(1-cosθ). At the lowest point, all this potential energy is converted to kinetic energy KE = ½mv². Setting PE = KE: mgL(1-cosθ) = ½mv². Solving for v: v² = 2gL(1-cosθ), so v = √(2gL(1-cosθ)), which corresponds to option A.