QuestionDecember 13, 2025

A typical compact disk has a mass of 15 g and a diameter of 120 mm. What is its moment of inertia about an axis through its center perpendicular to the disk? 2.7times 10^-5kgcdot m^2 5.4times 10^-5kgcdot m^2 1.1times 10^-4kgcdot m^2 2.2times 10^-4kgcdot m^2

A typical compact disk has a mass of 15 g and a diameter of 120 mm. What is its moment of inertia about an axis through its center perpendicular to the disk? 2.7times 10^-5kgcdot m^2 5.4times 10^-5kgcdot m^2 1.1times 10^-4kgcdot m^2 2.2times 10^-4kgcdot m^2
A typical compact disk has a mass of 15 g and a diameter of 120 mm. What is its moment of inertia about an axis through its center perpendicular to the disk? 2.7times 10^-5kgcdot m^2 5.4times 10^-5kgcdot m^2 1.1times 10^-4kgcdot m^2 2.2times 10^-4kgcdot m^2

Solution
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Answer

2.7\times 10^{-5}\,\text{kg}\cdot\text{m}^{2} Explanation 1. Convert Units Convert the diameter and mass to SI units (meters and kilograms). - Diameter d = 120\,\text{mm} = 0.12\,\text{m} - Radius r = \frac{d}{2} = \frac{0.12}{2} = 0.06\,\text{m} - Mass m = 15\,\text{g} = 0.015\,\text{kg} 2. Use Moment of Inertia Formula for a Disk The moment of inertia of a solid disk about its central axis is I = \frac{1}{2}mr^2. - Substitute values: \[ I = \frac{1}{2} \times 0.015 \times (0.06)^2 \] 3. Calculate the Moment of Inertia Perform the calculation step-by-step. - (0.06)^2 = 0.0036 - 0.015 \times 0.0036 = 0.000054 - \frac{1}{2} \times 0.000054 = 0.000027 So, \[ I = 2.7 \times 10^{-5}\,\text{kg}\cdot\text{m}^2 \]

Explanation

1. Convert Units<br /> Convert the diameter and mass to SI units (meters and kilograms).<br />- Diameter $d = 120\,\text{mm} = 0.12\,\text{m}$<br />- Radius $r = \frac{d}{2} = \frac{0.12}{2} = 0.06\,\text{m}$<br />- Mass $m = 15\,\text{g} = 0.015\,\text{kg}$<br /><br />2. Use Moment of Inertia Formula for a Disk<br /> The moment of inertia of a solid disk about its central axis is $I = \frac{1}{2}mr^2$.<br />- Substitute values:<br /> \[<br /> I = \frac{1}{2} \times 0.015 \times (0.06)^2<br /> \]<br /><br />3. Calculate the Moment of Inertia<br /> Perform the calculation step-by-step.<br />- $(0.06)^2 = 0.0036$<br />- $0.015 \times 0.0036 = 0.000054$<br />- $\frac{1}{2} \times 0.000054 = 0.000027$<br /><br />So,<br />\[<br />I = 2.7 \times 10^{-5}\,\text{kg}\cdot\text{m}^2<br />\]
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