## Essential University Physics: Volume 1 (4th Edition)

$2.1 \ m/s^2$
We know: $\omega^2 = \frac{g}{L}$ Thus, we find: $90^2 = \frac{g}{L}$ $1=\frac{g}{8100L}$ And $91^2 = \frac{\sqrt{g^2+a^2}}{L}$ $1 = \frac{g-a}{8281L}$ Setting these equal gives: $\frac{g}{8100L}= \frac{\sqrt{g^2+a^2}}{8281L}$ $a\approx2.1 \ m/s^2$