Problem

A standard CD has a diameter of 12 cm, and a hole that is centered on the axis of symmetry...

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.

Step-by-Step Solution

Solution 1

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

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