Answer
(a) 50 rad/s, 21.6 rad/s
(b) 5.55 km
(c) $-6.41\times10^{-3}rad/s^{2}$
Work Step by Step
(a) Here we use the equation $v=r\omega$ to find the angular velocity.
$v=r\omega=>\omega=\frac{v}{r}$ ; Let's plug known values into this equation.
$\omega_{1}=\frac{1.25\space m/s}{25\times10^{-3}m}=50\space rad/s$
$\omega_{2}=\frac{1.25\space m/s}{58\times10^{-3}m}=21.6\space rad/s$
(b) Track length = $(1.25\space m/s)(74\space min)(60\space s/min)=5.55\space km$
(c) Let's apply the equation $\omega=\omega_{0}+\alpha t$ to find the angular acceleration.
$\omega=\omega_{0}+\alpha t=>\alpha=\frac{\omega-\omega_{0}}{t}$
Let's plug known values into this equation.
$\alpha=\frac{21.55\space rad/s-50\space rad/s}{(74\space min)(60\space s/min)}=-6.41\times10^{-3}rad/s^{2}$
