Answer
We can rank the flywheels in order of their angular momentum, from smallest to largest:
$A = E = F \lt B \lt C \lt D$
Work Step by Step
We can find the angular momentum for each flywheel:
Flywheel A:
$L = I~\omega$
$L = \frac{1}{2}MR^2~\omega$
$L = \frac{1}{2}(10~kg)(0.20~m)^2~(30~rad/s)$
$L = 6.0~kg~m^2/s$
Flywheel B:
$L = I~\omega$
$L = \frac{1}{2}MR^2~\omega$
$L = \frac{1}{2}(20~kg)(0.20~m)^2~(30~rad/s)$
$L = 12.0~kg~m^2/s$
Flywheel C:
$L = I~\omega$
$L = \frac{1}{2}MR^2~\omega$
$L = \frac{1}{2}(20~kg)(0.40~m)^2~(15~rad/s)$
$L = 24.0~kg~m^2/s$
Flywheel D:
$L = I~\omega$
$L = \frac{1}{2}MR^2~\omega$
$L = \frac{1}{2}(20~kg)(0.40~m)^2~(30~rad/s)$
$L = 48.0~kg~m^2/s$
Flywheel E:
$L = I~\omega$
$L = \frac{1}{2}MR^2~\omega$
$L = \frac{1}{2}(20~kg)(0.10~m)^2~(60~rad/s)$
$L = 6.0~kg~m^2/s$
Flywheel F:
$L = I~\omega$
$L = \frac{1}{2}MR^2~\omega$
$L = \frac{1}{2}(5~kg)(0.20~m)^2~(60~rad/s)$
$L = 6.0~kg~m^2/s$
We can rank the flywheels in order of their angular momentum, from smallest to largest:
$A = E = F \lt B \lt C \lt D$
