TeXes Science Practice Test

Which equation represents rotational kinetic energy involving moment of inertia and angular velocity?

1. KEr = I ω

2. KEr = ½ I ω

3. KEr = ½ I ω²

4. KEr = I ω²

The correct answer is: KEr = ½ I ω²

The equation that represents rotational kinetic energy involving moment of inertia and angular velocity is given by KEr = ½ I ω². In this equation, KEr stands for rotational kinetic energy, I represents the moment of inertia, and ω (omega) is the angular velocity. This formula reflects the nature of rotational motion: just as linear kinetic energy depends on mass and the square of the velocity (KE = ½ mv²), rotational kinetic energy depends on how mass is distributed around an axis of rotation (moment of inertia) and the square of the angular velocity. The factor of ½ in front of I ω² signifies that kinetic energy in rotational motion involves not just the moment of inertia and angular velocity but also the scaling effect of the squared angular velocity, which significantly increases the energy as the speed of rotation increases. Understanding this equation is essential for analyzing systems in rotational dynamics, such as spinning disks or rotating machinery, and applies foundational principles of energy conservation in physics.