Rotational Kinetic Energy
Rotational kinetic energy is $K_{rot} = \tfrac{1}{2}I\omega^2$, the rotational twin of $K = \tfrac{1}{2}mv^2$. Doubling the angular velocity quadruples it, not doubles it. A flywheel on a fixed axle has zero translational KE by the 3.1 formula, yet it's clearly carrying energy; $K_{rot}$ is the formula that catches it. Same quadratic-in-the-speed trap as 3.1, restaged for a spinning body.
Three traps come up. Scaling $K_{rot}$ linearly with $\omega$, when doubling $\omega$ actually quadruples it. Reporting only $K_{trans}$ or only $K_{rot}$ for a rolling object, when the total carries both. Attaching a direction to $K_{rot}$, which is a scalar.
The work
3 ways in · any order
Lesson
Rotational Kinetic Energy
›
Build $K_{rot} = \tfrac{1}{2}I\omega^2$ as the rotational analog of $K = \tfrac{1}{2}mv^2$. Two worked examples: a spinning dumbbell, and a cylinder rolling down a ramp where translation and rotation share the energy budget. Ten-scenario applet hits the $\omega^2$ scaling trap, the $K_{trans} + K_{rot}$ bookkeeping trap, and the “$K_{rot}$ has a direction” scalar trap.
Diagnostic
10-item topic check
›
Ten multiple-choice items mapped to the misconception traps active in this topic. Each wrong answer is tied to a specific failure mode, so a miss tells you exactly which trap fired.
Targeted Practice
Drill a single misconception
›
Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.