Moment of Inertia of Disk at any point

In summary, the moment of inertia for a disc at any other point can be calculated using the parallel axis theorem, which takes into account the distance from the center of mass. This formula also applies to 3D shapes.
  • #1
TheDestroyer
402
1
As we know the moment of Inertia of a disc in the center of mass equals 0.5mr^2

My Simple question is: what is the moment of inertia of the disc at any other point? as I know there is a formula that supports the distance from the center of mass,

and is there a relation for 3D shapes?

Thanks
 
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  • #2
Do you know the parallel axis theorem?

The moment of inertia for an object rotating about an axis that does not pass through its centre of mass, but which is parallel to it, is

mr^2 + (moment of inertia about an axis through the centre of mass and parallel to the other axis)

The r is the distance from the axis to the centre of mass.
 
  • #3
Thank you, I know that law but this was 3 years ago, Thank you for reminding me, This post is closed!
 

1. What is moment of inertia of a disk at any point?

The moment of inertia of a disk at any point is a measure of its resistance to rotational motion. It takes into account the distribution of mass in the disk and the distance of each particle from the axis of rotation.

2. How is the moment of inertia of a disk at any point calculated?

The moment of inertia of a disk at any point can be calculated using the formula I = mr², where m is the mass of the disk and r is the distance of the point from the axis of rotation.

3. What factors affect the moment of inertia of a disk at any point?

The moment of inertia of a disk at any point is affected by the mass of the disk, the shape and size of the disk, and the distance of the point from the axis of rotation. It is also affected by the distribution of mass within the disk.

4. What is the significance of the moment of inertia of a disk at any point?

The moment of inertia of a disk at any point is an important concept in rotational motion as it determines how the disk will behave when subjected to a torque. It is also used in various engineering and physics applications.

5. How does the moment of inertia of a disk at any point compare to that of other shapes?

The moment of inertia of a disk at any point is typically lower than that of other shapes with the same mass, such as a cylinder or a sphere. This is because the mass in a disk is concentrated closer to the axis of rotation, resulting in a lower moment of inertia compared to a more spread-out mass distribution in other shapes.

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