A Yo$-$Yo with a Brain Yomega $("$The yo$-$yo with a brain"$)$ is constructed with a clever clutch mechanism in its axle that allows it to rotate freely and "sleep" when its angular speed is greater than a certain critical value. When the yo$-$yo's angular speed falls below this value, the clutch engages, causing the yo$-$yo to climb the string to the user's hand.

Part A

If the moment of inertia of the yo$-$yo is $7\mathrm{.}8105$ kg$$m$2$kg$$m$2,$ its mass is $0\mathrm{.}14$ kgkg $,$ and the string is $1\mathrm{.}4$ mm long, what is the smallest angular speed that will allow the yo$-$yo to return to the user's hand?

Express your answer using two significant figures.