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AP Physics C: Mechanics
7.5 Simple and Physical Pendulums
7.2 Frequency and Period of SHM
5.6 Newton’s Second Law in Rotational Form
5.4 Rotational Inertia
Multi-Unit
IntermediateMCQMathematical17.4k
A schematic diagram showing a torsional pendulum setup. At the top is a horizontal cross-hatched ceiling representing a fixed support. A single thin vertical solid line representing a wire extends downward from the center of the ceiling to the exact center of a horizontal disk. The disk is drawn as a flat horizontal ellipse with a shaded top surface, showing perspective. The radius of the disk is indicated by a horizontal dashed line extending from the center of the disk to its right edge, labeled R. Next to the disk, the mass is labeled M. A curved arrow wraps horizontally around the vertical wire just above the disk to indicate angular displacement, labeled \theta. Next to the wire, the torsion constant is labeled \kappa. No other labels, lines, text, or axes appear.
A uniform solid disk of mass M and radius R suspended by a vertical wire.
A torsional pendulum consists of a uniform solid disk of mass \(M\) and radius \(R\) suspended in a horizontal plane by a thin vertical wire attached to its center. When the disk is rotated through an angular displacement \(\theta\) from equilibrium, the wire exerts a restoring torque \(\tau = -\kappa\theta\), where \(\kappa\) is a positive constant. The disk is released from rest from an initial angular displacement \(\theta_0\). What is the period of rotational oscillation of the disk?

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