In general, with physics formulas, you plug the units right into the formulas. Say you're trying to find distance, and you have acceleration of 9.8m/s^2, and time of 4s:
d=1/2 a t^2
= 1/2 (9.8m/s^2)(4s)^2
= 1/2 (9.8m/s^2)(16s^2)
= 78.4m (the s^2 and 1/s^2 cancel out)
You can plug the units right into your formula as well, and get the correct units for moment of inertia out the other end.
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