#momentsofinertia

[utherciveng]

Geometric Characteristics

Moments of inertia

First moment of area = CENTROID x AREA = Static moment (Syo or Zyo)

Sx = ∫ydA = A*yc ---> yc = Sx/A (yc is the y coordinate of the centroid from the x axis)

Sy = ∫xdA = A*xc ---> xc = Sy/A (xc is the x coordinate of the centroid from the y axis)

Second moment of area; Area moment of inertia

Ix =  ∫∫y2dA (y is the coordinate of the object from the x-axis)

Iy = ∫∫x2dA (x is the coordinate of the object from the y-axis)

Moment of inertia; similar formula but different definition. Uses mass instead of area

Ix =  ∫y2dm (y is the coordinate of the object from the x-axis)

Iy = ∫x2dm (x is the coordinate of the object from the y-axis)

Units of moment of inertia is in [kg m2]

CM - Center of mass of an object.

Parallel Axis Theorem

I = ICM + Ad^2

ICM is the moment of inertia of an object relative to it's center from the analysed axis.

d is the perpendicular distance from an object's center to the axis.

A is the area.

Note: It normally helps to write the object center coordinates down on the diagram as you solve it.

Useful equations to know:

I always find it better to learn from examples. Below are 2 solved examples.

Oh yeah, happy Easter everyone! Hope y'all are having a good one.

Cheers

[pixiedustling]

Before the delicious mess*:. Getting down and dirty with my lover 💉🔪💉💉 #illicit #salome #moi #momentsofinertia #painproofpixie #ariel