Finding Area Moment of Inertia for Axis 33 to X-Axis

In summary, moment of inertia is a measure of an object's resistance to changes in its rotational motion. It takes into account the object's mass, distribution of mass, and shape. Unlike mass, two objects with the same mass can have different moments of inertia. Moment of inertia is calculated by summing the products of the mass of each infinitesimal element and the square of its distance from the axis of rotation. It is important in studying rotational motion and dynamics, calculating torque, assessing stability of structures, and understanding angular acceleration.
  • #1
rock.freak667
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Homework Statement


I have to find the area moment of inertia about an axis 33 to the x-axis
http://img227.imageshack.us/img227/2392/shape.jpg

Homework Equations


[tex]I_\phi=\frac{1}{2}(I_{xx}+I_{yy})+\frac{1}{2}(I{xx}-I_{yy})cos2\phi - I_{xy}sin2\phi[/tex]


The Attempt at a Solution



I found Ixx, but since it is symmetrical, Ixx=Iyy, and since it is symmetrical about the x and y axes, Ixy=0

So the I about any axis is just the 1/2(Ixx+Iyy) = Ixx.

Is my thinking correct, or am I mistaking it?
 
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  • #2
Looks ok to me.
 

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is also known as rotational inertia.

How is moment of inertia different from mass?

Moment of inertia is different from mass because it takes into account not only the mass of an object, but also its distribution of mass and its shape. This means that two objects with the same mass can have different moments of inertia if their mass is distributed differently.

What is axis 33 to X-axis?

Axis 33 to X-axis refers to a specific axis of rotation around an object. The 33 in this notation represents the direction of the axis, while the X-axis refers to the reference axis that the object is being rotated around.

How is the moment of inertia calculated?

The moment of inertia is calculated by summing the products of the mass of each infinitesimal element of an object and the square of its distance from the axis of rotation.

Why is finding the moment of inertia important?

Finding the moment of inertia is important in the study of rotational motion and dynamics. It is also necessary for calculating the amount of torque required to rotate an object, as well as for determining the stability of structures and the behavior of objects in angular acceleration.

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