# Realistic Value for the Rotational Inertia of a Gate

Don't worry guys i won't ask how to calculate the moment of inertia of the gate. I already have, but i have no experience in real life engineering, so i would be thankfull if any of you could review my result.

The Door wieghs about 90 kg Has a length of 3000 mm a height of 1115 mm and a width of 40 mm

I Calculated the Moment of Inertia on the hinges and the result was 227.5 kgm². I added a Picture so you can get an idea of how the gate looks like.

• Are you sure the unit is not kg m^2 Jan 7 '17 at 17:14
• To do a sanity check on your calculation, you might assume uniform weight distribution. Thus calculate the moment of inertial for a uniform 90 kg weight 3 meters long. By the way, is the calculation about the Z axis? Jan 7 '17 at 19:57
• ups sorry it is obviously kgm^2 Jan 8 '17 at 11:42
• Yes. The calculation is around the Z axis. Jan 8 '17 at 11:43

Your units are wrong. I think you meant $227.5\,\text{kg}\,\text{m}^2$.
From your calculations, the radius of gyration about the hinge is $$k = \sqrt{\frac I m} = \sqrt{\frac {227.5}{90}}\,\text{m} = 1590\,\text{mm}.$$
For a point mass at the middle of the gate, $k = 1500\,\text{mm}$.
For a uniformly distributed mass in the horizontal direction, $k = 3000/\sqrt3 = 1732\,\text{mm}$.
The design of your gate is somewhere in between those two limits, so $k = 1590\,\text{mm}$ is "not obviously wrong".