Question 9.11: Kinetic energy of a rolling wheel Find the kinetic energy of...

Assume the wheel to be uniform with mass M and radius b. Then its centre of mass C has speed u so that the translational kinetic energy is $\frac{1}{2} M u^{2}$. Because of the rolling condition, the angular velocity of the wheel is given by ω = u/b so that the rotational kinetic energy is $\frac{1}{2} I(u / b)^{2}, \text { where } I=\frac{1}{2} M b^{2}$. The total kinetic energy of the wheel is therefore given by

$T=\frac{1}{2} M u^{2}+\frac{1}{2}\left(\frac{1}{2} M b^{2}\right)\left(\frac{u}{b}\right)^{2}=\frac{3 M u^{2}}{4}.$