A solid cylinder with a mass $m$ and radius $r$ is mounted so that it can be rotated about an axis that passes through the center of both ends. At what angular speed $$ must the cylinder rotate to have the same total kinetic energy that it would have if it were moving horizontally with a speed $v$ without rotation?

$=\frac{v}{r}$

$=\frac{v^2}{r^2}$

$=\frac{v^2}{2r}$

$=\frac{v}{r}\sqrt[\phantom{2}]{2}$

$=\frac{v}{2r}$A solid cylinder with a mass $m$ and radius $r$ is mounted so that it can be rotated about an axis that passes through the center of both ends. At what angular speed $$ must the cylinder rotate to have the same total kinetic energy that it would have if it were moving horizontally with a speed $v$ without rotation?

$=\frac{v}{r}$

$=\frac{v^2}{r^2}$

$=\frac{v^2}{2r}$

$=\frac{v}{r}\sqrt[\phantom{2}]{2}$

$=\frac{v}{2r}$