Problem — Energy of a flywheel

Problem

A cylindrical flywheel of $M = 30\;\mathrm{kg}$, $R = 0{,}5\;\mathrm{m}$, rotates at $\omega = 100\;\mathrm{rad/s}$. Calculate the rotational kinetic energy.

Solution

Moment of inertia of the solid cylinder $I = \tfrac{1}{2}MR^2 = \tfrac{1}{2}\cdot 30\cdot 0{,}5^2 = 3{,}75\;\mathrm{kg\,m^2}$. Rotational kinetic energy: $E_k = \tfrac{1}{2}I\omega^2 = \tfrac{1}{2}\cdot 3{,}75\cdot 100^2 = \tfrac{1}{2}\cdot 3{,}75\cdot 10\,000$ $\ev{E_k \approx 1{,}88\cdot 10^4\;\mathrm{J} \approx 18{,}8\;\mathrm{kJ}}$ This is exactly how flywheels store energy: a lot of mass far from the axis and high speed build up useful kinetic energy to release when power peaks are needed.

Links

Topics: Rotational dynamics Concepts: Rotational kinetic energy · Moment of inertia Objects: Rotating disc