A simple pendulum of length swings with small angular displacements about its equilibrium
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A simple pendulum of length L=0.90m swings with small angular displacements about its equilibrium. A non-standard angular coordinate θ is defined so that θ is positive when the bob is displaced clockwise from the vertical rather than the usual counter-clockwise convention.
(a) Using this coordinate choice, express the restoring torque τ about the pivot in terms of m, g, L, and θ. State clearly the sign of each quantity where appropriate.
(b) Determine the direction (clockwise or counter-clockwise) of the angular acceleration when θ=+5∘ and the bob is instantaneously at rest.
(c) Explain how your expression in part (a) is consistent with the requirement for simple harmonic motion in rotational form.