## Essential University Physics: Volume 1 (3rd Edition)

We see how long it takes to get to 17 rpm: $\alpha=\frac{\tau}{I}=\frac{896,000\ Nm}{2.65\times10^7 \ kgm^2}=.034\ rads/s^2$ 17 rpm equals 1.78 radians per second, so it follows: $\Delta t =\frac{1.78\ rads/s}{.034\ rads/s^2}=53 \ seconds$ We now see about efficiency specifications: We find the power: $P=\frac{I\omega^2}{2t}=\frac{2(2.65\times10^7)(1.78)}{2(53)}=8.96\times10^5$ 96 percent of 1.5 is 1.41, not .896, so the turbine is not meeting efficiency specifications.