Question

The moment of inertia of a surface about an axis through its centroid is 4200 mm. if the area of the surface is 100 mm2, what will be the moment of inertia about a parallel axis 6mm distance from the centroid?​

Answer 1

Explanation:

3600mm

$3600 {mm}^{4}$

Answer 2

Answer:

Moment of inertia value is $7800$ $mm^{4}$.

Explanation:

• Moment of inertia about an axis parallel to the centroid is calculated by using the parallel axis theorem.
• The term used for the resistance of a body to the angular acceleration is called the moment of inertia.

The formula for the moment of inertia about a parallel axis to centroid:

$I_{XP} =I_{XC} +Ad^{2}$

where, $I_{XP}$ is inertia about a parallel axis.

            $I_{XC}$ is inertia about the centroid.

            $A$ is surface area.

            $d$ is the distance between centroid and axis.

Step 1:

Given values of $I_{XC} =4200$ $mm^{4}$

                          $A=100$ $mm^{2}$

                          $d= 6$ $mm$

Substitute values in the above formula:

Step 2:

$I_{XP} =4200+100 * 6^{2}$

$I_{XP} =7800$ $mm^{4}$

So, about the parallel axis, the moment of inertia is $7800$ $mm^{4}$.