Some dragonflies splash down onto the surface of a lake to clean themselves. After this dunking, the dragonflies gain altitude, and then spin rapidly at about 1100 rpm to spray the water off their bodies. When the dragonflies do this "spin-dry," they tuck themselves into a "ball" with a moment of inertia of 2.1×10−7kg⋅m2.

1/2(2.1*10^-7)(115.1917306)^2 =0.00139 kgm^2/s^2

2 answers

kgm^2/s^2
is also J for units
1/2 (2.1*10^-7)*[(2pi*1100/60)^2]
Dont forget to square the answer when you multiply 2pi with the conversion of rpm because it is essentially k=1/2 Iw^2

And use J for units