## College Physics (4th Edition)

We can rank the flywheels in order of linear speed at the rim, from largest to smallest: $c \gt a \gt d \gt b \gt e$
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: $c \gt a \gt d \gt b \gt e$