A standard CD has a diameter of 12 cm, and a hole that is centered on the axis of symmetry and has a diameter of 1.5 cm. The CD’s thickness is 2.0 mm. If a (very thin) pin extending through the hole of the CD suspends it in a vertical orientation, as shown in the figure, the CD may oscillate about an axis parallel to the pin, rocking back and forth. Calculate the oscillation frequency.

THINK:
We use the parallel axis theorem to find the moment of inertia and this can then used to find the oscillating frequency. Outer diameter of CD is
, inner diameter of CD is
and thickness of
RESEARCH:
Moment of inertia of CD is 
Radius of the CD is 
Angular speed of the CD is 
Frequency of the oscillator is 

From the parallel axis theorem, the moment of inertia is 
SIMPLIFY:
The moment of inertia is calculated as
Hence, the frequency of the oscillator is given by
CALCULATE:
Frequency of the oscillator is calculated as
