# Moment of inertia of T shape

• Dell
In summary, the conversation was about finding the moment of inertia for a T-shaped object using the parallel axis theorem. The individual provided the dimensions and distance from the centroid for the object, and then used both their own equation and one from a website to calculate the moment of inertia. However, they noticed a discrepancy between the two results and asked for help identifying where they went wrong.

#### Dell

h have a T shaped object (2-d) for which i need to find the moment of enertia,
i used a parallel axis theorem, then to check myself i found i site which had a direct equation for it
http://www.efunda.com/designstandards/beams/SquareTbeam.cfm

what i did

b1=100mm
h1=12mm
b2=12mm
h2=75mm
q=12.643mm(the distance from the joint of the 2 shapes to the centroid of the T)

>> ((b1*h1^3)/12)+((b1*h1)*(q+h1/2)^2)+((b2*h2^3)/12)+((b2*h2)*(h2/2-q)^2)

1.4094e-006 m4

using their equation

t=12mm
y=75-12.643=62.357mm
b=100mm
s=12mm
d=87mm

>> (t*y^3+b*(d-y)^3-(b-t)*(d-y-s)^3)/3

7.6247e-006m4

where have i gone wrong here?

sorry posted this in the wrong category

## 1. What is the formula for the moment of inertia of a T-shaped object?

The formula for the moment of inertia of a T-shaped object is I = I1 + I2 + Ad2, where I1 and I2 are the moments of inertia of the individual components of the T-shape and A is the area of the T-shape and d is the distance between the centroid of the T-shape and the centroid of the individual components.

## 2. How is the moment of inertia different from the center of mass of a T-shaped object?

The moment of inertia and the center of mass of a T-shaped object are two different physical quantities. The moment of inertia represents the object's resistance to rotational motion, while the center of mass represents the point at which an object's mass can be considered to be concentrated.

## 3. What factors affect the moment of inertia of a T-shaped object?

The factors that affect the moment of inertia of a T-shaped object include the object's mass, the distribution of mass within the object, and the distance between the centroid of the object and the axis of rotation. The shape and orientation of the object also play a role in determining its moment of inertia.

## 4. How does the moment of inertia of a T-shaped object impact its rotational motion?

The moment of inertia of a T-shaped object directly affects its rotational motion. A higher moment of inertia means that more force is required to accelerate the object into rotational motion. Similarly, a lower moment of inertia means that less force is required to rotate the object.

## 5. Can the moment of inertia of a T-shaped object be negative?

No, the moment of inertia cannot be negative. It is a physical quantity that represents the object's resistance to rotational motion and cannot have a negative value. However, the moment of inertia can be zero if the object has no mass or if all of its mass is located at the axis of rotation.