Final answer:
To calculate the polar moment of inertia for an I-beam, apply the parallel axis theorem on each component about the desired axis of rotation and then sum these moments of inertia.
Step-by-step explanation:
To find the polar moment of inertia for an I-beam, you need to use the parallel axis theorem. This theorem states that if you know the moment of inertia of a section about an axis through its center of mass (CM), you can find the moment of inertia about any parallel axis to this by adding the product of the mass of the section and the square of the distance from the CM axis to the new axis.
Here's the step-by-step guide:
- Calculate the moment of inertia for each component of the I-beam about their own center of mass (CM). This involves integrating or summing over every 'piece of mass' that makes up the part, multiplied by the square of the distance to the axis.
- Apply the parallel axis theorem to find the moment of inertia about the desired axis of rotation for each component. This involves adding the product of each component's mass and the square of the distance from its CM to the axis of rotation.
- Sum the moments of inertia of all individual components to obtain the total moment of inertia of the I-beam about the desired axis.
It's important to remember that the moment of inertia is an indication of how difficult it is to change the rotational state of an object about an axis.