## College Physics (4th Edition)

We can rank the flywheels in order of radial acceleration of a point at the rim, from largest to smallest: $c \gt d \gt a \gt b \gt e$
In general: $\omega = \frac{2\pi}{T}$ $v = \omega~r$ $a_c = \frac{v^2}{r}$ We can find the radial acceleration of a point at the rim of each flywheel: (a) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0040~s} = 1571~rad/s$ $v = (1571~rad/s)(0.080~m) = 125.7~m/s$ $a_c = \frac{(125.7~m/s)^2}{0.080~m} = 197,000~m^2/s$ (b) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0040~s} = 1571~rad/s$ $v = (1571~rad/s)(0.020~m) = 31.4~m/s$ $a_c = \frac{(31.4~m/s)^2}{0.020~m} = 49,000~m^2/s$ (c) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0010~s} = 6283~rad/s$ $v = (6283~rad/s)(0.080~m) = 502.6~m/s$ $a_c = \frac{(502.6~m/s)^2}{0.080~m} = 3,158,000~m^2/s$ (d) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0010~s} = 6283~rad/s$ $v = (6283~rad/s)(0.020~m) = 125.7~m/s$ $a_c = \frac{(125.7~m/s)^2}{0.020~m} = 790,000~m^2/s$ (e) $\omega = \frac{2\pi}{T} = \frac{2\pi}{0.0040~s} = 1571~rad/s$ $v = (1571~rad/s)(0.010~m) = 15.7~m/s$ $a_c = \frac{(15.7~m/s)^2}{0.010~m} = 25,000~m^2/s$ We can rank the flywheels in order of radial acceleration of a point at the rim, from largest to smallest: $c \gt d \gt a \gt b \gt e$