A disk is suspended by a nail such that the pivots in a vertical plane about a point on the edge of the disk.If the period of oscillation of the disk is 1.25 s ,what is the disk's radius?
A) 26 cm
B) 78 cm
C) Cannot answer without knowing the disk's mass
D) 51 cm

Question

Quizplus · Accepted Answer

The period of oscillation for a physical pendulum is given by $ T = 2\pi \sqrt{\frac{I}{mgd}} $, where $ I $ is the moment of inertia, $ m $ is the mass, $ g $ is the acceleration due to gravity, and $ d $ is the distance from the pivot to the center of mass. For a disk pivoting about its edge, $ I = \frac{3}{2}mr^2 $ and $ d = r $. Solving for $ r $ using the given period $ T = 1.25 $ s, we find $ r \approx 0.26 $ m or 26 cm. The mass cancels out, so it is not needed.

A Disk Is Suspended by a Nail Such That the Pivots