A Hoop, a Solid Cylinder, and a Solid Sphere All $\omega$

question 28

Multiple Choice

A hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is mounted to oscillate about an axis a distance 0.5 R from the centre. The axis is perpendicular to the circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below. Which is the correct ranking in order of increasing angular frequency $\omega$ ?

• A)hoop, cylinder, sphere
• B)cylinder, sphere, hoop
• C)sphere, cylinder, hoop
• D)hoop, sphere, cylinder
• E)sphere, hoop, cylinder

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Definitions:

Peak

The highest point or maximum value of a graph, often used in reference to spectra in analytical chemistry indicating a specific property.

C=C Stretching Frequency

Refers to the frequency at which the carbon-carbon double bonds in a molecule vibrate, typically observed in infrared spectroscopy.

IR Absorption

The absorption of infrared radiation by molecules, leading to changes in vibrational energy levels, used in spectroscopy to identify functional groups.

Intense IR Absorption

A characteristic of some materials to strongly absorb infrared radiation at specific wavelengths, indicative of particular molecular bonds.