Rotational Energy
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
A spinning object has kinetic energy because its parts are moving: Krot = ½Iω², the rotational version of ½mv². A torque that turns an object through an angle does work on it: W = τΔθ.
1. Spinning energy
2. Using it with energy conservation
Rotational kinetic energy is just another form of energy. Include it whenever something spins: a rolling ball, a pulley, a flywheel, a door.
Use ω in rad/s. Convert rpm or rev/s first.
A flywheel stores energy by spinning fast. Because K depends on ω², a small increase in spin rate stores a lot more energy.
3. Example, then try it
A flywheel with I = 0.40 kg·m² spins at 50 rad/s. How much kinetic energy does it store?
K = ½Iω² = ½(0.40)(50)² = 500 J.
A constant 5.0 N·m torque turns a wheel (I = 2.0 kg·m²) from rest through 20 rad. How fast is it spinning at the end?
Work done by the torque: W = τΔθ = (5.0)(20) = 100 J.
All of it becomes rotational kinetic energy: ½(2.0)ω² = 100.
Solve: ω² = 100 → ω = 10 rad/s.
Check with kinematics: α = 5.0 ÷ 2.0 = 2.5 rad/s²; ω² = 2αΔθ = 2(2.5)(20) = 100. ✓
Answer: 10 rad/s.
4. Common mistakes
Two wheels have the same rotational inertia. Wheel B spins 3 times as fast as wheel A. How does B’s rotational kinetic energy compare with A’s?
K = ½Iω². Tripling ω multiplies ω² by 9.
Ready to practice?
4 questions on Rotational Energy, each with a hint and an explanation for every wrong answer.