Physics

Problem

A solid uniform disk of mass

6.0\,\text{kg}

and radius

0.25\,\text{m}

starts from rest and rotates about its central axis with a constant angular acceleration of

4.0\,\text{rad/s}^2

. After the disk has turned through

300

revolutions, what is its rotational kinetic energy? a)

2.8\times 10^{3}\,\text{J}

1.4\times 10^{3}\,\text{J}

7.1\times 10^{2}\,\text{J}

2.3\times 10^{2}\,\text{J}

Intuitive explanation

The key is recognizing that you don't need to find the final angular velocity directly—instead, use the rotational kinematics equation to connect the angle rotated to angular velocity, then apply the rotational kinetic energy formula. For a solid disk, the moment of inertia $I = \frac{1}{2}mr^2$ is fixed, so once you know $\omega$ at 300 revolutions, you can calculate $KE_{\text{rot}} = \frac{1}{2}I\omega^2$ immediately.

Intuitive explanation

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