A ring of extremely dense material has a mass $M$ and a radius $R$. It spins at angular velocity $w$ $rad/s$. What is the kinetic energy, $KE$, stored in the ring? (Hint: start with the kinetic energy of a small particle translating at velocity, $V$, and integrate to form the ring rotating at angular velocity, $w$.)

A. $KE = (1/4) Mw^2R^2$
B. $KE = (1/2) Mw^2R^2$
C. $KE = (1/4) Mw^2R^3$
D. $KE = (1/4) Mw^3R^2$
E. None of the above