A simple pendulum consists of a small bob of mass attached to a light
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A simple pendulum consists of a small bob of mass m attached to a light, inextensible string of length L. The bob is displaced by a small angle θ0 from the vertical and released from rest. Throughout its subsequent motion the string remains taut and air resistance is negligible.
(1) Explain, without using detailed calculations, why the tangential component of the net force acting on the bob is proportional to its displacement from the equilibrium position when the angular displacement is small.
(2) Describe the geometric relationship between the bob’s linear displacement x along the arc of motion and its instantaneous angular displacement θ for small angles. Justify your reasoning.
(3) Discuss how the proportional tangential restoring force in the linear description corresponds to a proportional restoring torque in the angular description. In your answer, identify the physical quantity that plays the role of the “spring constant” for the angular representation.