Second Moment of Inertia of a Rectangle

Thread starter theBEAST
Start date Dec 6, 2012
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Inertia Moment Moment of inertia Rectangle

In summary, the second moment of inertia of a rectangle is a measure of its resistance to rotational motion around its central axis and is calculated by multiplying the length by the cube of its height and dividing by 12. It has units of length to the fourth power and affects the rotational motion of an object. In engineering and physics, it is important for calculations related to bending stress, deflection, stability, and understanding the motion of rigid bodies.

Dec 6, 2012

theBEAST

Homework Statement

Find the second moment of inertia of a rectangle.

The Attempt at a Solution

Anyone know why my answer is 4 times too big?

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Dec 6, 2012

rock.freak667

Homework Helper

Your limits of integration imply that your axis of references is the x-axis (which is correct by the way).

The "correct" answer you want is to get Ix about the centroidal axis. In which case your limits would be different.

Related to Second Moment of Inertia of a Rectangle

What is the second moment of inertia of a rectangle?

The second moment of inertia of a rectangle is a measure of the resistance of a rectangle to rotational motion around its central axis. It is also known as the moment of inertia or rotational inertia.

How is the second moment of inertia of a rectangle calculated?

The second moment of inertia of a rectangle can be calculated by multiplying the length of the rectangle by the cube of its height and dividing the result by 12. This formula assumes that the rectangle has a constant thickness.

What are the units of the second moment of inertia of a rectangle?

The units of the second moment of inertia of a rectangle are length to the fourth power, such as inches^4 or meters^4. This is because the calculation involves multiplying length by length squared.

How does the second moment of inertia of a rectangle affect its rotational motion?

The higher the second moment of inertia of a rectangle, the more difficult it is to rotate it around its central axis. This means that objects with a larger second moment of inertia will have a slower rotational motion compared to objects with a smaller second moment of inertia.

How is the second moment of inertia of a rectangle used in engineering and physics?

The second moment of inertia of a rectangle is an important property in the design and analysis of structures and machines that involve rotational motion. It is used in calculations related to bending stress, deflection, and stability. It is also utilized in physics to understand the motion of rigid bodies and their resistance to rotation.