Moment of Inertia for 2D Rectangle: Does it Depend on Both Sides?

In summary, the moment of inertia of a two dimensional rectangle with sides a and b, whose axis is parallel to one of its sides and passes through its center of mass, will not be (1/12)M(a2+b2). Instead, it will be (Ma2)/12 if the axis is parallel to one of the sides. This is because the lamina can be thought of as a set of parallel thin strips in the direction perpendicular to the axis, and adding more strips only increases the moment in proportion to the mass.
  • #1
peripatein
880
0
Hi,

Homework Statement


Will the moment of inertia of a two dimensional rectangle (with sides a, b) whose axis is parallel to one of its sides and passes through its center of mass, be (1/12)M(a2+b2)?


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
peripatein said:

Homework Statement


Will the moment of inertia of a two dimensional rectangle (with sides a, b) whose axis is parallel to one of its sides and passes through its center of mass, be (1/12)M(a2+b2)?
No. If the axis is, say, the y axis, think of the lamina as a set of parallel thin strips in the x direction. They'll all have the same moment. I think the formula you quoted would be right for an axis perpendicular to the lamina.
 
  • #3
But then wouldn't I be getting a moment of inertia equal to (Ma^2)/12 (supposing axis is parallel to a)?
 
  • #4
And what's wrong with that?
 
  • #5
It's not that something's wrong with that, simply that it seemed a bit strange it would not depend on the other side too.
 
  • #6
peripatein said:
It's not that something's wrong with that, simply that it seemed a bit strange it would not depend on the other side too.
That's why I said to think of it as parallel strips across the axis. Adding more only increases the moment in proportion to the mass.
 

FAQ: Moment of Inertia for 2D Rectangle: Does it Depend on Both Sides?

What is moment of inertia and why is it important?

Moment of inertia is a physical property that describes an object's resistance to changes in its rotational motion. It is important because it helps us understand how objects will behave when subjected to forces that cause rotational motion, such as torque.

How is moment of inertia calculated?

The moment of inertia of an object is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. The formula is I = mr^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

What factors affect the moment of inertia?

The moment of inertia is affected by the mass and distribution of mass of an object. Objects with more mass or with the mass distributed farther from the axis of rotation will have a larger moment of inertia.

How does moment of inertia differ from mass?

Moment of inertia and mass are two different physical properties. Mass is a measure of the amount of matter in an object, while moment of inertia is a measure of an object's resistance to rotational motion. An object can have the same mass but different moments of inertia depending on its shape and distribution of mass.

What are some practical applications of moment of inertia?

Moment of inertia has many practical applications, including in engineering, physics, and sports. It is used to design structures that can withstand rotational forces, such as bridges and buildings. In physics, it helps us understand the behavior of objects in rotational motion. In sports, it is important for activities such as gymnastics, figure skating, and diving.

Similar threads

Moment of inertia of a cuboid parallel to one of its faces (repost with diagram)
Replies
25
Views
1K
Moment of inertia of a disk about an axis not passing through its CoM
Replies
11
Views
2K
Moment of inertia of T bar about 3 axes
Replies
21
Views
2K
Moment of inertia of a rod bent into a square
Replies
12
Views
1K
Calculate the moment of inertia of this body
Replies
4
Views
1K
Moment of inertia of a disc using rods as differential elements
Replies
8
Views
1K
Question on Moment of Inertia Tensor of a Rotating Rigid Body
Replies
4
Views
1K
Finding the Moment of Inertia for a Rectangular Sheet
Replies
1
Views
3K
Quick question about moment of inertia
Replies
21
Views
2K
Calculating Moment of Inertia for a Curved Rod with Respect to a Specific Axis
Replies
1
Views
970

Hot Threads

Recent Insights

Back
Top