Answer
We can rank the flywheels in order of linear speed at the rim, from largest to smallest:
$c \gt a \gt d \gt b \gt e$
Work Step by Step
In general: $\omega = \frac{2\pi}{T}$
$v = \omega~r$
We can find the linear speed at the rim of each flywheel:
(a) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0040~s} = 1571~rad/s$
$v = (1571~rad/s)(0.080~m) = 125.7~m/s$
(b) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0040~s} = 1571~rad/s$
$v = (1571~rad/s)(0.020~m) = 31.4~m/s$
(c) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0010~s} = 6283~rad/s$
$v = (6283~rad/s)(0.080~m) = 502.6~m/s$
(d) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0020~s} = 3142~rad/s$
$v = (3142~rad/s)(0.020~m) = 62.8~m/s$
(e) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0040~s} = 1571~rad/s$
$v = (1571~rad/s)(0.010~m) = 15.7~m/s$
We can rank the flywheels in order of linear speed at the rim, from largest to smallest:
$c \gt a \gt d \gt b \gt e$
