Question

question 46
a dvd with a mass of 20 g a radius of 6.0 cm starts from rest and accelerates to an angular velocity of 24 rad/s in 1.2 s. assume the cd is a solid disk
what is the moment of inertia of the dvd? use table 9.1
○ 7.2 x 10⁻⁵ kg·m²
○ 7.2 x 10² kg·m²
○ 3.6 x 10² kg·m²
○ 3.6 x 10⁻⁵ kg·m²

Explanation:

Step1: Recall Moment of Inertia Formula for Solid Disk

The moment of inertia \( I \) for a solid disk (or a DVD, which we can model as a solid disk) is given by the formula \( I = \frac{1}{2}MR^2 \), where \( M \) is the mass of the disk and \( R \) is its radius.

Step2: Convert Units

First, convert the mass from grams to kilograms: \( M = 20\ \text{g} = 20 \times 10^{-3}\ \text{kg} = 0.02\ \text{kg} \).
Next, convert the radius from centimeters to meters: \( R = 6.0\ \text{cm} = 6.0 \times 10^{-2}\ \text{m} = 0.06\ \text{m} \).

Step3: Substitute Values into the Formula

Substitute \( M = 0.02\ \text{kg} \) and \( R = 0.06\ \text{m} \) into the formula \( I = \frac{1}{2}MR^2 \):

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Answer:

\( 3.6 \times 10^{-5}\ \text{kg·m}^2 \) (the option with this value)