Question

this final exam is cumulative and covers material from the entire course.
instructions
from the list of choices, select the one best answer.
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question 45 of 62
question 45
1.6 points
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 angular acceleration of the dvd?
29 rad/s²
26 rad/s²
20 rad/s²
24 rad/s²

Explanation:

Step1: Recall angular acceleration formula

Angular acceleration \(\alpha\) is given by the change in angular velocity (\(\Delta\omega\)) over time (\(t\)), so \(\alpha=\frac{\Delta\omega}{t}\).

Step2: Identify initial and final angular velocity

The DVD starts from rest, so initial angular velocity \(\omega_0 = 0\space rad/s\), final angular velocity \(\omega = 24\space rad/s\), and time \(t = 1.2\space s\).

Step3: Calculate change in angular velocity

\(\Delta\omega=\omega - \omega_0=24 - 0 = 24\space rad/s\).

Step4: Calculate angular acceleration

Substitute into the formula: \(\alpha=\frac{24}{1.2}=20\space rad/s^2\).

Answer:

\(20\space rad/s^2\) (corresponding to the option with "20 rad/s²")